First slide

Methods of integration

Question

$If \int \frac{x^{5 m - 1} + 2 x^{4 m - 1}}{{(x^{2 m} + x^{m} + 1)}^{3}} d x = f (x) + C then f (x) = 0$

Moderate

A

$\frac{x^{5 m}}{2 m {(x^{2 m} + x^{m} + 1)}^{2}}$
B

$\frac{2 m x^{5 m}}{x^{2 m} + x^{m} + 1}$
C

$\frac{x^{4 m}}{2 m {(x^{2 m} + x^{m} + 1)}^{2}}$
D

$\frac{2 m x^{4 m}}{x^{2 m} + x^{m} + 1}$

Solution

$\begin{array}{l} \int \frac{(x^{5 m - 1} + 2 x^{4 m - 1}) d x}{x^{6 m} {(1 + \frac{1}{x^{m}} + \frac{1}{x^{2 m}})}^{3}} \\ = \int \frac{(x^{- m - 1} + 2 x^{- 2 m - 1}) d x}{{(1 + x^{- m} + x^{- 2 m})}^{3}} \\ = \frac{- 1}{m} \int \frac{d t}{t^{3}} put t = 1 + x^{- m} + x^{- 2 m} \end{array}$
$\begin{array}{l} = \frac{- 1}{m} {(1 + x^{- m} + x^{- 2 m})}^{- 2} + C \\ = \frac{x^{4 m}}{2 m {(x^{2 m} + x^{m} + 1)}^{2}} + C \end{array}$

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