First slide

Methods of integration

Question

$\int \frac{{(x - x^{3})}^{1 / 3}}{x^{4}} d x$

Moderate

A

$\frac{3}{8} {(\frac{1}{x^{2}} - 1)}^{4 / 3} + C$
B

$\frac{- 3}{8} {(\frac{1}{x^{2}} - 1)}^{4 / 3} + C$
C

$\frac{3}{8} {(1 + \frac{1}{x^{2}})}^{4 / 3} + C$
D

$\frac{- 3}{8} {(1 + \frac{1}{x^{2}})}^{4 / 3} + C$

Solution

$\int \frac{x {[\frac{1}{x^{2}} - 1]}^{\frac{1}{3}}}{x^{4}} d x =$ $- \frac{1}{2} \int t^{\frac{1}{3}} d t$
$\frac{1}{x^{2}} - 1 = t \Rightarrow - \frac{2}{x^{3}} d x = d t$

$= - \frac{1}{2} \frac{t^{\frac{4}{3}}}{(\frac{4}{3})} + C$

$= - \frac{3}{8} {(\frac{1}{x^{2}} - 1)}^{\frac{4}{3}} + C$

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