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\int\frac{1}{\sqrt{x^2-36}}dx

Integral of 1/((x^2-36)^0.5)

Answer

$\ln\left(\frac{\sqrt{x^2-36}+x}{6}\right)+C_0$

Step-by-step explanation

Problem

$\int\frac{1}{\sqrt{x^2-36}}dx$
1

Solve the integral $\int\frac{1}{\sqrt{x^2-36}}dx$ by trigonometric substitution using the substitution

$\begin{matrix}x=6\sec\left(\theta\right) \\ dx=6\tan\left(\theta\right)\sec\left(\theta\right)d\theta\end{matrix}$

Unlock this step-by-step solution!

Answer

$\ln\left(\frac{\sqrt{x^2-36}+x}{6}\right)+C_0$
$\int\frac{1}{\sqrt{x^2-36}}dx$

Main topic:

Integration by trigonometric substitution

Used formulas:

6. See formulas

Time to solve it:

~ 3.24 seconds