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not stretchy integral subscript blank superscript blank fraction numerator left parenthesis 2 x plus 1 right parenthesis over denominator left parenthesis x to the power of 2 end exponent plus 4 x plus 1 right parenthesis to the power of 3 divided by 2 end exponent end fraction d x

  1. fraction numerator x to the power of 3 end exponent over denominator left parenthesis x to the power of 2 end exponent plus 4 x plus 1 right parenthesis to the power of fraction numerator 1 over denominator 2 end fraction end exponent end fraction plus C    
  2. fraction numerator x over denominator left parenthesis x to the power of 2 end exponent plus 4 x plus 1 right parenthesis to the power of fraction numerator 1 over denominator 2 end fraction end exponent end fraction plus C    
  3. fraction numerator x to the power of 2 end exponent over denominator left parenthesis x to the power of 2 end exponent plus 4 x plus 1 right parenthesis to the power of fraction numerator 1 over denominator 2 end fraction end exponent end fraction plus C    
  4. fraction numerator 1 over denominator left parenthesis x to the power of 2 end exponent plus 4 x plus 1 right parenthesis to the power of 1 divided by 2 end exponent end fraction plus C    

The correct answer is: fraction numerator x over denominator left parenthesis x to the power of 2 end exponent plus 4 x plus 1 right parenthesis to the power of fraction numerator 1 over denominator 2 end fraction end exponent end fraction plus C

Related Questions to study

General
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The equation of the directrix of the parabola y to the power of 2 end exponent plus 4 y plus 4 x plus 2 equals 0 comma i s colon

The equation of the directrix of the parabola y to the power of 2 end exponent plus 4 y plus 4 x plus 2 equals 0 comma i s colon

maths-General
General
Maths-

The equation of the common tangent touching the circle left parenthesis x minus 3 right parenthesis to the power of 2 end exponent plus y to the power of 2 end exponent equals 9 and the parabola y to the power of 2 end exponent equals 4 x above the x‐axis is:

The equation of the common tangent touching the circle left parenthesis x minus 3 right parenthesis to the power of 2 end exponent plus y to the power of 2 end exponent equals 9 and the parabola y to the power of 2 end exponent equals 4 x above the x‐axis is:

Maths-General
General
Maths-

If the line x‐1 =0 is the directrix of the parabola y to the power of 2 end exponent minus k x plus 8 equals 0, then one of the values of k is :

If the line x‐1 =0 is the directrix of the parabola y to the power of 2 end exponent minus k x plus 8 equals 0, then one of the values of k is :

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General
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Assertion (A): Three normals are drawn from the point P’ with slopes m subscript 1 end subscript comma m subscript 2 end subscript comma m subscript 3 end subscript to the parabola y to the power of 2 end exponent equals 4 x If locus of ‘ P’ with m subscript 1 end subscript m subscript 2 end subscript equals alpha is a part of the parabola itself then alpha equals 2
Reason (R): If normals at left parenthesis x subscript 1 end subscript comma y subscript 1 end subscript right parenthesis comma left parenthesis x subscript 2 end subscript comma y subscript 2 end subscript right parenthesis and left parenthesis y subscript 3 end subscript comma y subscript 3 end subscript right parenthesis are concurrent then y subscript 1 end subscript plus y subscript 2 end subscript plus y subscript 3 end subscript equals 0

Assertion (A): Three normals are drawn from the point P’ with slopes m subscript 1 end subscript comma m subscript 2 end subscript comma m subscript 3 end subscript to the parabola y to the power of 2 end exponent equals 4 x If locus of ‘ P’ with m subscript 1 end subscript m subscript 2 end subscript equals alpha is a part of the parabola itself then alpha equals 2
Reason (R): If normals at left parenthesis x subscript 1 end subscript comma y subscript 1 end subscript right parenthesis comma left parenthesis x subscript 2 end subscript comma y subscript 2 end subscript right parenthesis and left parenthesis y subscript 3 end subscript comma y subscript 3 end subscript right parenthesis are concurrent then y subscript 1 end subscript plus y subscript 2 end subscript plus y subscript 3 end subscript equals 0

maths-General
General
maths-

ABCD and EFGC are squares and the curve y equals k square root of x passes through the origin D and the points B and F The ratio fraction numerator F G over denominator B C end fraction is:

ABCD and EFGC are squares and the curve y equals k square root of x passes through the origin D and the points B and F The ratio fraction numerator F G over denominator B C end fraction is:

maths-General
General
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Statement‐I :: With respect to a hyperbola fraction numerator x to the power of 2 end exponent over denominator 9 end fraction minus fraction numerator y to the power of 2 end exponent over denominator 16 end fraction equals 1 pependicular are drawn from a point (5, 0) on the lines 3 y plus-or-minus 4 x equals 0, then their feet lie on circle x to the power of 2 end exponent plus y to the power of 2 end exponent equals 16.
Statement‐II :: If from any foci of a hyperbola perpendicular are drawn on the asymptotes of the hyperbola then their feet lie on auxiliary circle.

Statement‐I :: With respect to a hyperbola fraction numerator x to the power of 2 end exponent over denominator 9 end fraction minus fraction numerator y to the power of 2 end exponent over denominator 16 end fraction equals 1 pependicular are drawn from a point (5, 0) on the lines 3 y plus-or-minus 4 x equals 0, then their feet lie on circle x to the power of 2 end exponent plus y to the power of 2 end exponent equals 16.
Statement‐II :: If from any foci of a hyperbola perpendicular are drawn on the asymptotes of the hyperbola then their feet lie on auxiliary circle.

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General
maths-

A hyperbola, having the transverse axis of length 2 s i n, is confocal with the ellipse 3 x to the power of 2 end exponent plus 4 y to the power of 2 end exponent equals 12 Then its equation is ‐

A hyperbola, having the transverse axis of length 2 s i n, is confocal with the ellipse 3 x to the power of 2 end exponent plus 4 y to the power of 2 end exponent equals 12 Then its equation is ‐

maths-General
General
Maths-

The latus rectum of the hyperbola 16 x to the power of 2 end exponent minus 9 y to the power of 2 end exponent equals 144 is‐

The latus rectum of the hyperbola 16 x to the power of 2 end exponent minus 9 y to the power of 2 end exponent equals 144 is‐

Maths-General
General
maths-

Statement‐I :: If a point open parentheses x subscript 1 end subscript comma blank y subscript 1 end subscript close parentheses lies in the shaded region fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction minus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1, show in the figure, then fraction numerator x subscript 1 end subscript superscript 2 end superscript over denominator a to the power of 2 end exponent end fraction minus fraction numerator y subscript 1 end subscript superscript 2 end superscript over denominator b to the power of 2 end exponent end fraction less than 0
Statement‐II :: P left parenthesis x subscript 1 end subscript comma blank y subscript 1 end subscript right parenthesis lies outside the hyperbola fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction minus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1, then fraction numerator x subscript 1 end subscript superscript 2 end superscript over denominator a to the power of 2 end exponent end fraction minus fraction numerator y subscript 1 end subscript superscript 2 end superscript over denominator b to the power of 2 end exponent end fraction less than 1.

Statement‐I :: If a point open parentheses x subscript 1 end subscript comma blank y subscript 1 end subscript close parentheses lies in the shaded region fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction minus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1, show in the figure, then fraction numerator x subscript 1 end subscript superscript 2 end superscript over denominator a to the power of 2 end exponent end fraction minus fraction numerator y subscript 1 end subscript superscript 2 end superscript over denominator b to the power of 2 end exponent end fraction less than 0
Statement‐II :: P left parenthesis x subscript 1 end subscript comma blank y subscript 1 end subscript right parenthesis lies outside the hyperbola fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction minus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1, then fraction numerator x subscript 1 end subscript superscript 2 end superscript over denominator a to the power of 2 end exponent end fraction minus fraction numerator y subscript 1 end subscript superscript 2 end superscript over denominator b to the power of 2 end exponent end fraction less than 1.

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General
Maths-

Statement‐I The ellipse fraction numerator x to the power of 2 end exponent over denominator 16 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 9 end fraction equals 1 and fraction numerator x to the power of 2 end exponent over denominator 9 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 16 end fraction equals 1 are congruent.
Statement‐II The ellipse fraction numerator x to the power of 2 end exponent over denominator 16 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 9 end fraction equals 1 and fraction numerator x to the power of 2 end exponent over denominator 9 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 16 end fraction equals 1 have the same eccentricity.

For such questions, we should know properties of ellipse. We should know all the formulas related to ellipse. The axis which is larger is always the major axis.

Statement‐I The ellipse fraction numerator x to the power of 2 end exponent over denominator 16 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 9 end fraction equals 1 and fraction numerator x to the power of 2 end exponent over denominator 9 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 16 end fraction equals 1 are congruent.
Statement‐II The ellipse fraction numerator x to the power of 2 end exponent over denominator 16 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 9 end fraction equals 1 and fraction numerator x to the power of 2 end exponent over denominator 9 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 16 end fraction equals 1 have the same eccentricity.

Maths-General

For such questions, we should know properties of ellipse. We should know all the formulas related to ellipse. The axis which is larger is always the major axis.

General
Maths-

The minimum area of triangle formed by tangent to the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1 and coordinate axes‐

The minimum area of triangle formed by tangent to the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1 and coordinate axes‐

Maths-General
General
Maths-

An ellipse has OB as semi minor axis, F and F to the power of † end exponent its focii and the angle FBF’ is a right angle Then the eccentricity of the ellipse is‐

Therefore, the eccentricity of the ellipse isspace space fraction numerator 1 over denominator square root of 2 end fraction

An ellipse has OB as semi minor axis, F and F to the power of † end exponent its focii and the angle FBF’ is a right angle Then the eccentricity of the ellipse is‐

Maths-General

Therefore, the eccentricity of the ellipse isspace space fraction numerator 1 over denominator square root of 2 end fraction

parallel
General
Maths-

The number of values of c such that the straight line y=4x+c touches the curve left parenthesis x to the power of 2 end exponent divided by 4 right parenthesis plus y to the power of 2 end exponent equals 1 is‐

Therefore, there are two values of c.

The number of values of c such that the straight line y=4x+c touches the curve left parenthesis x to the power of 2 end exponent divided by 4 right parenthesis plus y to the power of 2 end exponent equals 1 is‐

Maths-General

Therefore, there are two values of c.

General
Maths-

Let P be any point on any directrix of an ellipse Then the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at

Let P be any point on any directrix of an ellipse Then the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at

Maths-General
General
maths-

An ellipse having foci at (3, 3) and (-4,4) and passing through the origin has eccentricity equal to‐

An ellipse having foci at (3, 3) and (-4,4) and passing through the origin has eccentricity equal to‐

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