First slide

Introduction to integration

Question

$\int \frac{x^{3}}{x + 1} d x$

Easy

A

$x + \frac{x^{2}}{2} + \frac{x^{3}}{3} - \ln |x + 1| + C$
B

$x - \frac{x^{2}}{2} - \frac{x^{3}}{3} - \ln |x + 1| + C$
C

$x + \frac{x^{2}}{2} - \frac{x^{3}}{3} - \ln |x + 1| + C$
D

$\frac{x^{3}}{3} - \frac{x^{2}}{2} + x - \ln |x + 1| + C$

Solution

$\int \frac{x^{3}}{x + 1} d x = \int \frac{x^{3} + 1 - 1}{x + 1} d x = \int \frac{x^{3} + 1}{x + 1} d x + \int \frac{- 1}{x + 1} d x = \int (x^{2} - x + 1) d x - \int \frac{1}{x + 1} d x = \frac{x^{3}}{3} - \frac{x^{2}}{2} + x - \ln |x + 1| + C$

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