x 3 x + 1 d x is equal to:

Question

$\int \frac{x^{3}}{x + 1} d x$ is equal to:

Smart Achievers · Accepted Answer

(4)

Ans. $x - \frac{x^{2}}{2} + \frac{x^{3}}{3} - \log$ $| 1 + x |$ $+ C$

Explanation:

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

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

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

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

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

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