First slide

Methods of integration

Question

$The integral \int \frac{d x}{(x + 4)^{\frac{8}{7}} (x - 3)^{\frac{6}{7}}} is equal to: (where C is a constant of integration)$

Moderate

A

$- \frac{1}{13} {(\frac{x - 3}{x + 4})}^{- 13 / 7} + C$
B

${(\frac{x - 3}{x + 4})}^{1 / 7} + C$
C

$- {(\frac{x - 3}{x + 4})}^{1 / 7} + C$
D

$\frac{1}{2} {(\frac{x - 3}{x + 4})}^{3 / 7} + C$

Solution

$\begin{array}{l} Let I = \int {(\frac{x - 3}{x + 4})}^{\frac{- 6}{7}} \frac{1}{(x + 4)^{2}} d x \\ Put \frac{x - 3}{x + 4} = t^{7} \Rightarrow \frac{7}{(x + 4)^{2}} d x = 7 t^{6} d t \\ So, I = \int t^{- 6} t^{6} d t = t + c = {(\frac{x - 3}{x + 4})}^{\frac{1}{7}} + c \end{array}$

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