Evaluate the following integrals:
Question:

Evaluate: $\int \frac{x^{3}-1}{x^{2}} d x$

Solution:

Given, $\int \frac{x^{2}-1}{x^{2}} d x$

$=\int \frac{x^{3}}{x^{2}}-\frac{1}{x^{2}} d x$

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

$\left[\right.$ since, $\left.\int x^{n} d x=\frac{x^{n+1}}{n+1}\right]$

$=\frac{x^{2}}{2}-\frac{x^{-2+1}}{-2+1}+c$

$=\frac{x^{2}}{2}-\frac{x^{-1}}{-1}+c$

$=\frac{x^{2}}{2}+\frac{1}{x}+c$

Administrator

Leave a comment

Please enter comment.
Please enter your name.