e^x≤ft(1/x-1/x²) - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

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

Question : 152 of 271

Marks: +1, -0

e^x\left(\frac{1}{x}-\frac{1}{x^2}\right)

Solution:

Let

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

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

=e^x\times\frac{1}{x}+C

=\frac{e^x}{x}+C

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

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