Math virtual assistant

About Snapxam Calculators Topics Go Premium
ENGESP
Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/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

\int\frac{x^2}{\sqrt{x^2-6}}dx

Integral of (x^2)/((x^2-6)^0.5)

Answer

$6\left(\frac{1}{2}\left(\ln\left(\sqrt{x^2-6}+x\right)-\frac{3}{\sqrt{2}}\right)+\frac{\frac{1}{12}\sqrt{x^2-6}x^{2}}{x}\right)+C_0$

Step-by-step explanation

Problem

$\int\frac{x^2}{\sqrt{x^2-6}}dx$
1

Solve the integral $\int\frac{x^2}{\sqrt{x^2-6}}dx$ by trigonometric substitution using the substitution

$\begin{matrix}x=\sqrt{5}\sec\left(\theta\right) \\ dx=\sqrt{5}\tan\left(\theta\right)\sec\left(\theta\right)d\theta\end{matrix}$

Unlock this step-by-step solution!

Answer

$6\left(\frac{1}{2}\left(\ln\left(\sqrt{x^2-6}+x\right)-\frac{3}{\sqrt{2}}\right)+\frac{\frac{1}{12}\sqrt{x^2-6}x^{2}}{x}\right)+C_0$

Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!