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Maths-

General

Easy

Question

The value of $lambda$ for which $not stretchy integral fraction numerator 4 x to the power of 3 end exponent plus lambda 4 to the power of x end exponent over denominator 4 to the power of x end exponent plus x to the power of 4 end exponent end fraction$ dx = log (4^x + x⁴) is -

1
log _e4
log ₄e
4

The correct answer is: log _e4

4^x + x⁴ = t
 (4x³ + 4^x ln e⁴) dx = dt
 $not stretchy integral fraction numerator d t over denominator t end fraction$ = log |t| + c
$table row cell therefore lambda equals log subscript e end subscript invisible function application 4 end cell end table$

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