Q85 / 150 · MHT CET 2007 · Mathematics

$\int \cos ^{3} x \cdot e^{\log (\sin x)} d x$ is equal to

  • A
    $-\frac{\sin ^{4} x}{4}+c$
  • Correct answer
    B
    $-\frac{\cos ^{4} x}{4}+c$
  • C
    $\frac{e^{\sin x}}{4}+c$
  • D
    None of these

Solution

Let $I=\int \cos ^{3} x e^{\log \sin x} d x=\int \cos ^{3} x \sin x d x$ Put $x=t \quad \Rightarrow-\sin x d x=d t$ $$ I=-\int t^{3} d t=-\frac{t^{4}}{4}+c=-\frac{\cos ^{4} x}{4}+c $$

Hence, the correct answer is option: 'B'.

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