MHT CET · Maths · Indefinite Integration
\(\int \cos ^{3} x \cdot e^{\log (\sin x)} d x\) is equal to
- A \(-\frac{\sin ^{4} x}{4}+c\)
- B \(-\frac{\cos ^{4} x}{4}+c\)
- C \(\frac{e^{\sin x}}{4}+c\)
- D None of these
Answer & Solution
Correct Answer
(B) \(-\frac{\cos ^{4} x}{4}+c\)
Step-by-step Solution
Detailed explanation
Let \(I=\int \cos ^{3} x e^{\log \sin x} d x=\int \cos ^{3} x \sin x d x\)
Put \(x=t \quad \Rightarrow-\sin x d x=d t\)
\(
I=-\int t^{3} d t=-\frac{t^{4}}{4}+c=-\frac{\cos ^{4} x}{4}+c
\)
Put \(x=t \quad \Rightarrow-\sin x d x=d t\)
\(
I=-\int t^{3} d t=-\frac{t^{4}}{4}+c=-\frac{\cos ^{4} x}{4}+c
\)
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