Math virtual assistant

Calculators Topics Go Premium About Snapxam
ENGESP

Step-by-step Solution

Integral of $\frac{1}{\sqrt{\left(1+x^2\right)^3}}$ with respect to x

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
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

Answer

$\frac{x}{\sqrt{1+x^2}}+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{1}{\sqrt{\left(1+x^2\right)^3}}dx$
1

Applying the power of a power property

$\int\frac{1}{\sqrt{\left(1+x^2\right)^{3}}}dx$
2

Solve the integral $\int\frac{1}{\sqrt{\left(1+x^2\right)^{3}}}dx$ by trigonometric substitution using the substitution

$\begin{matrix}x=1\tan\left(\theta\right) \\ dx=\sec\left(\theta\right)^2d\theta\end{matrix}$

Unlock this step-by-step solution!

Answer

$\frac{x}{\sqrt{1+x^2}}+C_0$
$\int\frac{1}{\sqrt{\left(1+x^2\right)^3}}dx$

Main topic:

Integrals of Rational Functions

Used formulas:

7. See formulas

Time to solve it:

~ 1.0 seconds