Find the Integral 7/( square root of x)

$\frac{7}{\sqrt{x}}$

Since $7$ is constant with respect to $x$ , move $7$ out of the integral.

$7 \int \frac{1}{\sqrt{x}} d x$

Apply basic rules of exponents.

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

$7 \int \frac{1}{x^{\frac{1}{2}}} d x$

Move $x^{\frac{1}{2}}$ out of the denominator by raising it to the $- 1$ power.

$7 \int {(x^{\frac{1}{2}})}^{- 1} d x$

Multiply the exponents in ${(x^{\frac{1}{2}})}^{- 1}$ .

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Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$7 \int x^{\frac{1}{2} \cdot - 1} d x$

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

$7 \int x^{\frac{- 1}{2}} d x$

Move the negative in front of the fraction.

$7 \int x^{- \frac{1}{2}} d x$

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

$7 (2 x^{\frac{1}{2}} + C)$

Simplify the answer.

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Simplify.

$7 (2 x^{\frac{1}{2}}) + C$

Multiply $2$ by $7$ .

$14 x^{\frac{1}{2}} + C$

Find the Integral 7/( square root of x)

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