First slide

Introduction to integration

Question

$\int x^{5} {(1 + x^{3})}^{2 / 3} d x = A {(1 + x^{3})}^{8 / 3} + B {(1 + x^{3})}^{5 / 3} + c, then$

Moderate

A

$A = \frac{1}{4}, B = \frac{1}{5}$
B

$A= \frac{1}{8}, B = - \frac{1}{5}$
C

$A=- \frac{1}{8}, B = \frac{1}{5}$
D

None of these

Solution

$\begin{array}{l} Let 1 + x^{3} = t^{2} \Rightarrow 3 x^{2} d x = 2 t d t \\ ∴ \int x^{5} {(1 + x^{3})}^{2 / 3} d x = \int x^{3} {(1 + x^{3})}^{2 / 3} x^{2} d x \\ = \int (t^{2} - 1) {(t^{2})}^{2 / 3} x^{2} d x \\ = \frac{2}{3} \int (t^{2} - 1) t^{7 / 3} d t \\ = \frac{2}{3} \int (t^{13 / 3} - t^{7 / 3}) d t \\ = \frac{2}{3} \{\frac{3}{16} t^{163} - \frac{3}{10} t^{10 / 3}\} + c \\ = \frac{1}{8} {(1 + x^{3})}^{8 / 3} - \frac{1}{5} {(1 + x^{3})}^{5 / 3} + c \end{array}$

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