Calculus Examples

$\frac{50}{3 \int u^{\frac{3}{2}} d u}$

Step 1

By the Power Rule, the integral of $u^{\frac{3}{2}}$ with respect to $u$ is $\frac{2}{5} u^{\frac{5}{2}}$ .

$\frac{50}{3 (\frac{2}{5} u^{\frac{5}{2}} + C)}$

Step 2

Simplify the answer.

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Step 2.1

Rewrite $\frac{50}{3 (\frac{2}{5} u^{\frac{5}{2}} + C)}$ as $\frac{50}{3 (\frac{2}{5}) u^{\frac{5}{2}}} + C$ .

$\frac{50}{3 (\frac{2}{5}) u^{\frac{5}{2}}} + C$

Step 2.2

Simplify.

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Step 2.2.1

Combine $3$ and $\frac{2}{5}$ .

$\frac{50}{\frac{3 \cdot 2}{5} u^{\frac{5}{2}}} + C$

Step 2.2.2

Multiply $3$ by $2$ .

$\frac{50}{\frac{6}{5} u^{\frac{5}{2}}} + C$