# Integration by trigonometric substitution Calculator

## Get detailed solutions to your math problems with our Integration by trigonometric substitution 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 Integration by trigonometric substitution

$\int\sqrt{x^2-4}dx$
2

Solve the integral $\int\sqrt{x^2-4}dx$ by trigonometric substitution using the substitution

$\begin{matrix}x=2\sec\left(\theta\right) \\ dx=\frac{d}{d\theta}\left(2\sec\left(\theta\right)\right)d\theta\end{matrix}$
3

Substituting in the original integral, we get

$\int\sqrt{4\sec\left(\theta\right)^2-4}\cdot\frac{d}{d\theta}\left(2\sec\left(\theta\right)\right)d\theta$
4

Factor by the greatest common divisor $4$

$\int\sqrt{4\left(\sec\left(\theta\right)^2-1\right)}\cdot\frac{d}{d\theta}\left(2\sec\left(\theta\right)\right)d\theta$
5

The power of a product is equal to the product of it's factors raised to the same power

$\int2\sqrt{\sec\left(\theta\right)^2-1}\cdot\frac{d}{d\theta}\left(2\sec\left(\theta\right)\right)d\theta$
6

Applying the trigonometric identity: $\tan\left(\theta\right)^2=\sec\left(\theta\right)^2-1$

$\int2\tan\left(\theta\right)\frac{d}{d\theta}\left(2\sec\left(\theta\right)\right)d\theta$
7

Take the constant out of the integral

$2\int\tan\left(\theta\right)\frac{d}{d\theta}\left(2\sec\left(\theta\right)\right)d\theta$