Calculus Examples

$\int 3 \sin^{- 2} (x) d x$

Step 1

This integral could not be completed using u-substitution. Mathway will use another method.

Step 2

Simplify.

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Step 2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\int 3 \frac{1}{\sin^{2} (x)} d x$

Step 2.2

Rewrite $1$ as $1^{2}$ .

$\int 3 \frac{1^{2}}{\sin^{2} (x)} d x$

Step 2.3

Rewrite $\frac{1^{2}}{\sin^{2} (x)}$ as ${(\frac{1}{\sin (x)})}^{2}$ .

$\int 3 {(\frac{1}{\sin (x)})}^{2} d x$

Step 2.4

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\int 3 \csc^{2} (x) d x$

Step 3

Since $3$ is constant with respect to $x$ , move $3$ out of the integral.

$3 \int \csc^{2} (x) d x$

Step 4

Since the derivative of $- \cot (x)$ is $\csc^{2} (x)$ , the integral of $\csc^{2} (x)$ is $- \cot (x)$ .

$3 (- \cot (x) + C)$

Step 5

Simplify the answer.

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Step 5.1

Simplify.

$3 (- \cot (x)) + C$

Step 5.2

Multiply $- 1$ by $3$ .

$- 3 \cot (x) + C$