AP EAMCET · Maths · Indefinite Integration
\(\int \frac{\cos ^3(x)}{\sin ^2(x)+\sin (x)} d x=\)
- A \(\log |\sin (x)|+\sin (x)+c\)
- B \(\log |\sin (x)|+\cos (x)+c\)
- C \(\log |\cos (x)|-\sin (x)+c\)
- D \(\log |\sin (x)|-\sin (x)+c\)
Answer & Solution
Correct Answer
(D) \(\log |\sin (x)|-\sin (x)+c\)
Step-by-step Solution
Detailed explanation
\begin{aligned} I & =\int \frac{\cos ^3 x}{\sin ^2 x+\sin x} \cdot d x \\ & =\int \frac{\left(1-\sin ^2 x\right) \cos x}{\sin ^2 x+\sin x} \cdot d x \\ \sin x & =t \Rightarrow \cos x d x=d t \\ \therefore \quad I & =\int \frac{1-t^2}{t^2+t} \cdot d t=\int…
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