Calculus Examples

\csc^{2} (x)

$\csc^{2} (x)$

Step 1

Write

\csc^{2} (x)

$\csc^{2} (x)$ as a function.

f (x) = \csc^{2} (x)

$f (x) = \csc^{2} (x)$

Step 2

The function

F (x)

$F (x)$ can be found by finding the indefinite integral of the derivative

f (x)

$f (x)$ .

F (x) = \int f (x) d x

$F (x) = \int f (x) d x$

Step 3

Set up the integral to solve.

F (x) = \int \csc^{2} (x) d x

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

Step 4

Since the derivative of

- \cot (x)

$- \cot (x)$ is

\csc^{2} (x)

$\csc^{2} (x)$ , the integral of

\csc^{2} (x)

$\csc^{2} (x)$ is

- \cot (x)

$- \cot (x)$ .

- \cot (x) + C

$- \cot (x) + C$

Step 5

The answer is the antiderivative of the function

f (x) = \csc^{2} (x)

$f (x) = \csc^{2} (x)$ .

F (x) =

$F (x) =$

- \cot (x) + C

$- \cot (x) + C$

\csc^{2} x

$\csc^{2} x$

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