First slide

Methods of integration

Question

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

Easy

A

$\frac{1 + x}{1 - x}$
B

$\frac{1 - x}{1 + x}$
C

$\frac{1 + x}{x - 1}$
D

$\frac{x - 1}{x + 1}$

Solution

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

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

     $= e^{x} | \frac{1 + x}{1 - x} | + c$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App