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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 20

Answers (1)

Answer :

e^{x}(1-\cot x)+c


Simplify it and integrate it.


\begin{aligned} &I=\int e^{x}\left(1-\cot x+\operatorname{cosec}^{2} x\right) d x\\ \end{aligned}

\begin{aligned} &\operatorname{Asf}(x)=1-\cot x\\ \end{aligned}      …(i)

\begin{aligned} &\Rightarrow f^{\prime}(x)=\operatorname{cosec}^{2} x \end{aligned}

We will use the formula   I=\int e^{x}\left(f(x)+f^{\prime}(x)\right) d x \Rightarrow I=e^{x} f(x)+c

\Rightarrow I=e^{x}(1-\cot x)+c    …from equi (i)


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