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Maths-

General

Easy

Question

$not stretchy integral fraction numerator d x over denominator sec to the power of 2 end exponent invisible function application x plus tan to the power of 2 end exponent invisible function application x end fraction$ is equal to

$\sqrt{2} \tan^{- 1} (\sqrt{2} \tan x) + x + c$
$\sqrt{2} \tan^{- 1} (\sqrt{2} \tan x) - x + c$
$\sqrt{2} \tan^{- 1} (2 \tan x) + c$
none of these

The correct answer is: $square root of 2 tan to the power of negative 1 end exponent invisible function application open parentheses square root of 2 tan invisible function application x close parentheses minus x plus c$

$not stretchy integral fraction numerator d x over denominator sec to the power of 2 end exponent invisible function application x plus tan to the power of 2 end exponent invisible function application x end fraction$
$equals not stretchy integral fraction numerator sec to the power of 2 end exponent invisible function application x minus tan to the power of 2 end exponent invisible function application x over denominator sec to the power of 2 end exponent invisible function application x plus tan to the power of 2 end exponent invisible function application x end fraction d x equals not stretchy integral fraction numerator 2 sec to the power of 2 end exponent invisible function application x minus left parenthesis sec to the power of 2 end exponent invisible function application x plus tan to the power of 2 end exponent invisible function application x right parenthesis over denominator sec to the power of 2 end exponent invisible function application x plus tan to the power of 2 end exponent invisible function application x end fraction d x$
$equals 2 not stretchy integral fraction numerator sec to the power of 2 end exponent invisible function application x over denominator sec to the power of 2 end exponent invisible function application x plus tan to the power of 2 end exponent invisible function application x end fraction d x minus not stretchy integral d x equals 2 not stretchy integral fraction numerator sec to the power of 2 end exponent invisible function application x d x over denominator 1 plus 2 tan to the power of 2 end exponent invisible function application x end fraction minus x plus c$
$equals not stretchy integral fraction numerator sec to the power of 2 end exponent invisible function application x d x over denominator fraction numerator 1 over denominator 2 end fraction plus tan to the power of 2 end exponent invisible function application x end fraction minus x plus c$
Put tan x = z\sec²x dx = dz
\given integral $equals not stretchy integral fraction numerator d z over denominator fraction numerator 1 over denominator 2 end fraction plus z to the power of 2 end exponent end fraction minus x plus c$
$equals fraction numerator 1 over denominator fraction numerator 1 over denominator square root of 2 end fraction end fraction tan to the power of negative 1 end exponent invisible function application fraction numerator z over denominator fraction numerator 1 over denominator square root of 2 end fraction end fraction minus x plus c equals square root of 2 tan to the power of negative 1 end exponent invisible function application left parenthesis square root of 2 z right parenthesis minus x plus c$
$equals square root of 2 tan to the power of negative 1 end exponent invisible function application open parentheses square root of 2 tan invisible function application x close parentheses minus x plus c$

Related Questions to study

Let $f left parenthesis x right parenthesis equals not stretchy integral e to the power of x end exponent left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis d x$ . Then f decreases in the interval :

Let $f left parenthesis x right parenthesis equals not stretchy integral e to the power of x end exponent left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis d x$ . Then f decreases in the interval :

The function f(x) = | px − q|+ r|x|, $x element of left parenthesis negative infinity comma infinity right parenthesis$ ,where p > 0, q > 0, r > 0, assumes its minimum value only at one point if :

The function f(x) = | px − q|+ r|x|, $x element of left parenthesis negative infinity comma infinity right parenthesis$ ,where p > 0, q > 0, r > 0, assumes its minimum value only at one point if :

The number of solutions of the equation x³ + 2x² + 5x + 2 cos x = 0 in [0, 2 $pi$ ] is :

The number of solutions of the equation x³ + 2x² + 5x + 2 cos x = 0 in [0, 2 $pi$ ] is :

parallel

The distance between the origin and the normal to the curve y = e^2x + x² at the point x = 0 is :

The distance between the origin and the normal to the curve y = e^2x + x² at the point x = 0 is :

The function f(x) = (x² − 1) |x² − 3x + 2 | + cos | x |) is not differentiable at :

The function f(x) = (x² − 1) |x² − 3x + 2 | + cos | x |) is not differentiable at :

If x^y y^x = 1, then $fraction numerator d y over denominator d x end fraction$ is :

If x^y y^x = 1, then $fraction numerator d y over denominator d x end fraction$ is :

parallel

If g(x) is a polynomial such that g(x) g(y) = g(x) + g(y) + g(xy) − 2 for all real x and y and g(2) = 5, then $stack l i m with x rightwards arrow 2 below g ´ left parenthesis x right parenthesis$ is :

If g(x) is a polynomial such that g(x) g(y) = g(x) + g(y) + g(xy) − 2 for all real x and y and g(2) = 5, then $stack l i m with x rightwards arrow 2 below g ´ left parenthesis x right parenthesis$ is :

$CH subscript 3 CH equals CHCH subscript 3 plus KCl plus straight H subscript 2 straight O$ Dehydrohalogenation reaction of 2-chlorobutane gives 2-butene.
(R) Elimination reaction takes' place according to Saytzeff's rule.

$CH subscript 3 CH equals CHCH subscript 3 plus KCl plus straight H subscript 2 straight O$ Dehydrohalogenation reaction of 2-chlorobutane gives 2-butene.
(R) Elimination reaction takes' place according to Saytzeff's rule.

Chemistry-General

(R) -CN is an ambident nucleophile, therefore, reaction gives both cyanide and isocyanide.

(R) -CN is an ambident nucleophile, therefore, reaction gives both cyanide and isocyanide.

Chemistry-General

parallel

If 1,3-dibromopropane reacts with zinc and NaI, the product. obtained is : .

If 1,3-dibromopropane reacts with zinc and NaI, the product. obtained is : .

Chemistry-General

In the following reaction, .

The major product obtained is :

In the following reaction, .

The major product obtained is :

Chemistry-General

For the following reaction,

product [A] is:

For the following reaction,

product [A] is:

Chemistry-General

parallel

When 2-chloro-2-methylbutane is heated with alcoholic KOH, the possible product/s is/are:
i) $open parentheses C H subscript 3 end subscript close parentheses subscript 2 end subscript C equals C H C H subscript 3 end subscript$
ii) $H subscript 2 end subscript C equals stack C with bar on top open parentheses C H subscript 3 end subscript close parentheses stack C with bar on top H subscript 2 end subscript C H subscript 3 end subscript$
iii) $open parentheses C H subscript 3 end subscript close parentheses subscript 2 end subscript C H C H equals C H subscript 2 end subscript$

When 2-chloro-2-methylbutane is heated with alcoholic KOH, the possible product/s is/are:
i) $open parentheses C H subscript 3 end subscript close parentheses subscript 2 end subscript C equals C H C H subscript 3 end subscript$
ii) $H subscript 2 end subscript C equals stack C with bar on top open parentheses C H subscript 3 end subscript close parentheses stack C with bar on top H subscript 2 end subscript C H subscript 3 end subscript$
iii) $open parentheses C H subscript 3 end subscript close parentheses subscript 2 end subscript C H C H equals C H subscript 2 end subscript$

Chemistry-General

(A) predominantly is:

(A) predominantly is:

Chemistry-General

Ethyl chloride on reduction with $L i A l H subscript 4 end subscript$ gives compound , X' as an important product. 'X' on chlorination with one mole of Cl₂ in the presence of light at ordinary temperature gives' Y'. What is 'Y' ?

Ethyl chloride on reduction with $L i A l H subscript 4 end subscript$ gives compound , X' as an important product. 'X' on chlorination with one mole of Cl₂ in the presence of light at ordinary temperature gives' Y'. What is 'Y' ?

Chemistry-General

parallel

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