First slide

Methods of integration

Question

$\int \frac{d x}{x (x^{4} + 1)}$ is equal to

Easy

A

$\frac{1}{4} \log \frac{x^{4} + 1}{x^{4}} + C$
B

$\frac{1}{4} \log (\frac{x^{4}}{x^{4} + 1}) + C$
C

$\frac{1}{4} \log (x^{4} + 1) + C$
D

none of these

Solution

$\int \frac{d x}{x (x^{4} + 1)} = \frac{1}{4} \int \frac{4 x^{3} d x}{x^{4} (x^{4} + 1)}$
$\begin{aligned} = \frac{1}{4} \int \frac{d t}{t (t + 1)} (t = x^{4}) \\ = \frac{1}{4} \int (\frac{1}{t} - \frac{1}{t + 1}) d t = \frac{1}{4} \log \frac{x^{4}}{x^{4} + 1} + C . \end{aligned}$

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