Step-by-step Solution

Integrate $\sqrt{x^2-4}$ with respect to x

Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
÷
2

e
π
ln
log
log
lim
d/dx
Dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Videos

$\frac{1}{2}\sqrt{x^2-4}x-2\ln\left|\frac{x+\sqrt{x^2-4}}{2}\right|+C_0$

Step-by-step explanation

Problem to solve:

$\int_{ }^{ }\left(\sqrt{\left(x^2-4\right)}\right)dx$
1

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

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

Substituting in the original integral, we get

$\int2\sqrt{4\sec\left(\theta\right)^2-4}\sec\left(\theta\right)\tan\left(\theta\right)d\theta$

$\frac{1}{2}\sqrt{x^2-4}x-2\ln\left|\frac{x+\sqrt{x^2-4}}{2}\right|+C_0$
$\int_{ }^{ }\left(\sqrt{\left(x^2-4\right)}\right)dx$

Main topic:

Integration by trigonometric substitution

13. See formulas

~ 1.0 seconds