(x-3)e^x/(x-1)³ - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

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

Question : 153 of 271

Marks: +1, -0

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

Solution:

Let

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

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

= \int e^x\left[\frac{1}{(x-1)^2} - \frac{2}{(x-1)^3}\right]dx

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

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

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

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