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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 8

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 8

Answers (1)

Answer:

\frac{e^{x}}{x+1}+c

Hint:

Simplify the function and then integrate it with the help of formula.

Solution:

\begin{aligned} &I=\int \frac{x e^{x}}{(x+1)^{2}} d x \\ &I=\int e^{x}\left[\frac{x+1-1}{(x+1)^{2}}\right] d x \\ &I=\int e^{x}\left[\frac{1}{x+1}-\frac{1}{(x+1)^{2}}\right] d x \end{aligned}

 

As we know that,  \int\left[f(x)+f^{\prime}(x)\right] e^{x} d x=f(x) e^{x}+c

 

I=e^{x} \frac{1}{x+1}+c

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