TS EAMCET · Maths · Indefinite Integration
\(\int \operatorname{cosec}^5 x d x=\)
- A \(\frac{\operatorname{cosec} x \cot ^3 x}{4}-\frac{5}{8} \operatorname{cosec} x \cot x+\frac{3}{8} \log\) \[ \left|\tan \frac{x}{2}\right|+c \]
- B \(-\frac{\operatorname{cosec} x \cot ^3 x}{4}-\frac{5}{8} \operatorname{cosec} x \cot x\) \[ +\frac{3}{8} \log \left|\tan \frac{x}{2}\right|+c \]
- C \(-\frac{\operatorname{cosec}^3 x \cot x}{4}-\frac{3}{8} \operatorname{cosec} x \cot x\) \[ +\frac{3}{8} \log \left|\tan \frac{x}{2}\right|+c \]
- D \(-\frac{\operatorname{cosec}^3 x \cot x}{4}+\frac{3}{8} \operatorname{cosec} x \cot x-\frac{3}{8} \log\) \[ \left|\tan \frac{x}{2}\right|+c \]
Answer & Solution
Correct Answer
(C) \(-\frac{\operatorname{cosec}^3 x \cot x}{4}-\frac{3}{8} \operatorname{cosec} x \cot x\) \[ +\frac{3}{8} \log \left|\tan \frac{x}{2}\right|+c \]
Step-by-step Solution
Detailed explanation
\[ \text { } \begin{aligned} I & =\int \operatorname{cosec}^5 x d x=\int \operatorname{cosec}^3 x \cdot \operatorname{cosec}^2 x d x \\ & =\operatorname{cosec}^3 x(-\cot x)-\int(-\cot x) 3 \operatorname{cosec}^2 x \end{aligned} \]…
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