First slide

Methods of integration

Question

$The value of the integral \int (x^{2} + x) {(x^{- 8} + 2 x^{- 9})}^{1 / 10} d x is$

Moderate

A

$\frac{5}{11} {(x^{2} + 2 x)}^{11 / 10} + c$
B

$\frac{5}{6} (x + 1)^{11 / 10} + c$
C

$\frac{6}{7} (x + 1)^{11 / 10} + c$
D

$None of these$

Solution

$\begin{array}{l} I = \int (x^{2} + x) {(x^{- 8} + 2 x^{- 9})}^{1 / 10} d x \\ = \int (x + 1) {(x^{2} + 2 x)}^{1 / 10} d x \\ Put x^{2} + 2 x = t \Rightarrow (x + 1) d x = \frac{d t}{2} \\ Now, I = \int t^{\frac{1}{10}} \cdot \frac{d t}{2} = \frac{1}{2} \times \frac{10}{11} t^{\frac{11}{10}} = \frac{5}{11} t^{\frac{11}{10}} + c \\ ∴ I = \frac{5}{11} {(x^{2} + 2 x)}^{\frac{11}{10}} + c \end{array}$

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