First slide

Methods of integration

Question

$\int \frac{x^{3} - 1}{x^{3} + x} d x is equal to$

Moderate

A

$x - \log_{e} | x | + \log_{e} (x^{2} + 1) - \tan^{- 1} x + C$
B

$x - \log_{e} | x | + \frac{1}{2} \log_{e} (x^{2} + 1) - \tan^{- 1} x + C$
C

$x + \log_{e} | x | + \frac{1}{2} \log_{e} (x^{2} + 1) + \tan^{- 1} x + C$
D

$none of these$

Solution

$\begin{aligned} \int \frac{x^{3} - 1}{x^{3} + x} d x = \int (1 - \frac{1}{1 + x^{2}} - \frac{1}{x} + \frac{x}{x^{2} + 1}) d x \\ = x - \tan^{- 1} x - \log_{e} | x | + \frac{1}{2} \log_{e} (x^{2} + 1) + C \end{aligned}$

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