Calculus Examples

$\int 3 u \frac{1}{2} d u$

Step 1

Simplify.

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Step 1.1

Combine $3$ and $\frac{1}{2}$ .

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

Step 1.2

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

$\int \frac{u \cdot 3}{2} d u$

Step 1.3

Move $3$ to the left of $u$ .

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

Step 2

Since $\frac{3}{2}$ is constant with respect to $u$ , move $\frac{3}{2}$ out of the integral.

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

Step 3

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

$\frac{3}{2} (\frac{1}{2} u^{2} + C)$

Step 4

Simplify the answer.

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Step 4.1

Rewrite $\frac{3}{2} (\frac{1}{2} u^{2} + C)$ as $\frac{3}{2} \cdot \frac{1}{2} u^{2} + C$ .

$\frac{3}{2} \cdot \frac{1}{2} u^{2} + C$

Step 4.2

Simplify.

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Step 4.2.1

Multiply $\frac{3}{2}$ by $\frac{1}{2}$ .

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

Step 4.2.2

Multiply $2$ by $2$ .

$\frac{3}{4} u^{2} + C$