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CBSE Class 12 · 2024 · Indefinite IntegralsShort Answer

Find

\int cos^{3} x e^{l o g s i n x} d x

Answer: $- \frac{cos ^{4} x}{4} + C$

Solution

Since

e^{l o g s i n x} = sin x

, the integral is

\int cos^{3} x sin x d x .

Put

t = cos x

,

d t = - sin x d x

:

\int t^{3} (- d t) = - \frac{t ^{4}}{4} + C .

- \frac{cos ^{4} x}{4} + C

CBSE Class 12 Board · 2024 · Subjective

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