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  • provide solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.26 question 10

provide solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.26 question 10

Answers (1)

best_answer

Answer:
The correct answer is \frac{e^{x}}{(x+1)^{2}}+c
Given:

\int e^{x} \frac{x-1}{(x+1)^{3}} d x

Solution:

        I=\int e^{x} \frac{x-1}{(x+1)^{3}} d x

        \mathrm{I}=\int\left\{\frac{x+1-2}{(x+1)^{3}}\right\} e^{x} d x

           =\int\left\{\frac{1}{(x+1)^{2}}-\frac{2}{(x+1)^{8}}\right\} e^{x} d x

           =\int e^{x} \frac{1}{(x+1)^{2}} d x-2 \int e^{x} \frac{1}{(x+1)^{3}} d x

On using Integration by parts,

            =\left\{\frac{1}{(x+1)^{2}} \cdot e^{x}-\int e^{x} \frac{-2}{(x+1)^{3}} d x\right\}-2 \int e^{x} \frac{1}{(x+1)^{3}} d x

            =\frac{e^{x}}{(x+1)^{2}}+c

So, the correct answer  \frac{e^{x}}{(x+1)^{2}}+c

 

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