Calculus Examples

$7^{3} \sqrt{x}$

Step 1

Raise $7$ to the power of $3$ .

$\int 343 \sqrt{x} d x$

Step 2

Since $343$ is constant with respect to $x$ , move $343$ out of the integral.

$343 \int \sqrt{x} d x$

Step 3

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$343 \int x^{\frac{1}{2}} d x$

Step 4

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

$343 (\frac{2}{3} x^{\frac{3}{2}} + C)$

Step 5

Simplify the answer.

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Step 5.1

Rewrite $343 (\frac{2}{3} x^{\frac{3}{2}} + C)$ as $343 (\frac{2}{3}) x^{\frac{3}{2}} + C$ .

$343 (\frac{2}{3}) x^{\frac{3}{2}} + C$

Step 5.2

Simplify.

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Step 5.2.1

Combine $343$ and $\frac{2}{3}$ .

$\frac{343 \cdot 2}{3} x^{\frac{3}{2}} + C$

Step 5.2.2

Multiply $343$ by $2$ .

$\frac{686}{3} x^{\frac{3}{2}} + C$