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  • Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.26 question 9 maths textbook solution

Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.26 question 9 maths textbook solution

Answers (1)

Answer:
The correct answer is e^{x} \log (\sin x)+c
Hint:

\int e^{x}\left\{f(x)+f^{\prime}(x)\right\} d x=e^{x} f(x)+c

Given:

Solution:

        \int e^{x}(\cot x+\log \sin x) d x

        \begin{aligned} &f(x)=\log (\sin x) \\ &f^{\prime}(x)=\frac{1}{\sin x} \cdot \cos x=\cot x \end{aligned}

        \begin{aligned} &\int e^{x}\left\{f(x)+f^{\prime}(x)\right\} d x=e^{x} f(x)+c \\ &\int e^{x}\left[(\cot x+\log (\sin x)] d x=e^{x} \log (\sin x)+\mathrm{c}\right. \end{aligned}

So, the correct answer is e^{x} \log (\sin x)+c

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