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

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

Hint:

Simplify it and integrate it.

Solution:

\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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