# Trigonometric integrals Calculator

## Get detailed solutions to your math problems with our Trigonometric integrals step by step calculator. Sharpen your math skills and learn step by step with our math solver. Check out more online calculators here.

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### Difficult Problems

1

Solved example of Trigonometric integrals

$\int\left(\sec\left(x\right)^6-\sec\left(x\right)^4\right)dx$
2

The integral of a sum of two or more functions is equal to the sum of their integrals

$\int\sec\left(x\right)^6dx+\int-\sec\left(x\right)^4dx$
3

Take the constant out of the integral

$\int\sec\left(x\right)^6dx-\int\sec\left(x\right)^4dx$
4

Simplify the integral of secant applying the reduction formula, $\displaystyle\int\sec(x)^{n}dx=\frac{\sin(x)\sec(x)^{n-1}}{n-1}+\frac{n-2}{n-1}\int\sec(x)^{n-2}dx$

$\frac{\sec\left(x\right)^{5}\sin\left(x\right)}{5}+\frac{6-2}{6-1}\int\sec\left(x\right)^{\left(6-2\right)}dx-\int\sec\left(x\right)^4dx$
5

Subtract the values $6$ and $-2$

$\frac{\sec\left(x\right)^{5}\sin\left(x\right)}{5}+\frac{4}{5}\int\sec\left(x\right)^{4}dx-\int\sec\left(x\right)^4dx$
6

Divide $4$ by $5$

$\frac{\sec\left(x\right)^{5}\sin\left(x\right)}{5}+\frac{4}{5}\int\sec\left(x\right)^{4}dx-\int\sec\left(x\right)^4dx$
7

Adding $\frac{4}{5}\int\sec\left(x\right)^{4}dx$ and $-1\int\sec\left(x\right)^{4}dx$

$\frac{\sec\left(x\right)^{5}\sin\left(x\right)}{5}-\frac{1}{5}\int\sec\left(x\right)^{4}dx$
8

Simplify the integral of secant applying the reduction formula, $\displaystyle\int\sec(x)^{n}dx=\frac{\sin(x)\sec(x)^{n-1}}{n-1}+\frac{n-2}{n-1}\int\sec(x)^{n-2}dx$

$\frac{\sec\left(x\right)^{5}\sin\left(x\right)}{5}-\frac{1}{5}\left(\frac{\sec\left(x\right)^{3}\sin\left(x\right)}{3}+\frac{2}{3}\int\sec\left(x\right)^{2}dx\right)$
9

The integral of $\sec(x)^2$ is $\tan(x)$

$\frac{\sec\left(x\right)^{5}\sin\left(x\right)}{5}-\frac{1}{5}\left(\frac{\sec\left(x\right)^{3}\sin\left(x\right)}{3}+\frac{2}{3}\tan\left(x\right)\right)$
10

As the integral that we are solving is an indefinite integral, when we finish we must add the constant of integration

$\frac{\sec\left(x\right)^{5}\sin\left(x\right)}{5}-\frac{1}{5}\left(\frac{\sec\left(x\right)^{3}\sin\left(x\right)}{3}+\frac{2}{3}\tan\left(x\right)\right)+C_0$