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Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise  Revision Exercise Question 120 Maths Textbook Solution

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Answer: I=e^{x} \frac{1}{\tan ^{2} x}+C

Hint: to solve this equation, we have to break the \left(1+x^{2}\right)

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


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

I=\int e^{x} \frac{1}{1+x^{2}}-\frac{2 x}{\left(1+x^{2}\right)^{2}} d x \ldots \int e^{x}\left(f^{\prime}(x)+f(x) d x=e^{x} f(x)+C\right.

I=e^{x} \frac{1}{1+x^{2}}+C

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