x e^x/(1+x)² - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.6
Integrate the functions in Exercises 134 to 155.

Question : 150 of 271

Marks: +1, -0

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

Solution:

Let

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

\Rightarrow I = \int e^x \left[ \frac{1+x-1}{(1+x)^2} \right] dx

\Rightarrow I = \int e^x \left[ \frac{1}{1+x} - \frac{1}{(1+x)^2} \right] dx

\Rightarrow I = \int e^x \left[ \frac{1}{1+x} + \left( \frac{d}{dx} \left( \frac{1}{1+x} \right) \right) \right] dx

\Rightarrow I = \left[ e^x \cdot \frac{1}{1+x} + C \right]

\left[ \because \int e^x (f(x)+f'(x)) dx = e^x f(x) + C \right]

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