Calculus Examples

\frac{- 6}{\sqrt{1 - x^{2}}}

$\frac{- 6}{\sqrt{1 - x^{2}}}$

Step 1

Move the negative in front of the fraction.

\int - \frac{6}{\sqrt{1 - x^{2}}} d x

$\int - \frac{6}{\sqrt{1 - x^{2}}} d x$

Step 2

Since

- 1

$- 1$ is constant with respect to

x

$x$ , move

- 1

$- 1$ out of the integral.

- \int \frac{6}{\sqrt{1 - x^{2}}} d x

$- \int \frac{6}{\sqrt{1 - x^{2}}} d x$

Step 3

Since

6

$6$ is constant with respect to

x

$x$ , move

6

$6$ out of the integral.

- (6 \int \frac{1}{\sqrt{1 - x^{2}}} d x)

$- (6 \int \frac{1}{\sqrt{1 - x^{2}}} d x)$

Step 4

Write the expression using exponents.

Tap for more steps...

Step 4.1

Multiply

6

$6$ by

- 1

$- 1$ .

- 6 \int \frac{1}{\sqrt{1 - x^{2}}} d x

$- 6 \int \frac{1}{\sqrt{1 - x^{2}}} d x$

Step 4.2

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

- 6 \int \frac{1}{\sqrt{1^{2} - x^{2}}} d x

$- 6 \int \frac{1}{\sqrt{1^{2} - x^{2}}} d x$

- 6 \int \frac{1}{\sqrt{1^{2} - x^{2}}} d x

$- 6 \int \frac{1}{\sqrt{1^{2} - x^{2}}} d x$

Step 5

The integral of

\frac{1}{\sqrt{1^{2} - x^{2}}}

$\frac{1}{\sqrt{1^{2} - x^{2}}}$ with respect to

x

$x$ is

arcsin (x)

$\arcsin (x)$

- 6 (arcsin (x) + C)

$- 6 (\arcsin (x) + C)$

Step 6

Simplify.

- 6 arcsin (x) + C

$- 6 \arcsin (x) + C$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$