AP EAMCET · Maths · Indefinite Integration
\(\int \frac{\sin 7 x}{\sin 2 x \sin 5 x} d x=\)
- A \(\log (\sin 5 x \sin 2 x)+c\)
- B \(\log \sin 5 x+\sin 2 x+c\)
- C \(\frac{1}{5} \log \sin 5 x+\frac{1}{2} \log \sin 2 x+c\)
- D \(\frac{1}{5} \log \sin x+\frac{1}{2} \log \sin x+c\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{5} \log \sin 5 x+\frac{1}{2} \log \sin 2 x+c\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & I=\int \frac{\sin 7 x}{\sin 2 x \sin 5 x} d x \Rightarrow I=\int \frac{\sin (5 x+2 x)}{\sin 2 x \sin 5 x} d x \\ & \Rightarrow I=\int \frac{\sin 5 x \cos 2 x+\cos 5 x \sin 2 x}{\sin 2 x \sin 5 x} d x \\ & \Rightarrow I=\int \cot 2 x d x+\int \cot 5 x d x \\ &…
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