Calculus Examples

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

Step 1

By the Power Rule, the integral of $x^{- \frac{3}{2}}$ with respect to $x$ is $- 2 x^{- \frac{1}{2}}$ .

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

Step 2

Simplify the answer.

Tap for more steps...

Step 2.1

Rewrite $- 2 x^{- \frac{1}{2}} + C$ as $- 2 \frac{1}{x^{\frac{1}{2}}} + C$ .

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

Step 2.2

Simplify.

Tap for more steps...

Step 2.2.1

Combine $- 2$ and $\frac{1}{x^{\frac{1}{2}}}$ .

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

Step 2.2.2

Move the negative in front of the fraction.

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