Math virtual assistant

Calculators Topics Go Premium About Snapxam
ENGESP

Step-by-step Solution

Integral of $\frac{8x+8}{\left(x-1\right)^3\left(x^2+1\right)}$ 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

Answer

$4arctan\left(x\right)+\frac{4}{x-1}+\frac{-4}{\left(x-1\right)^{2}}+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{8x+8}{\left(x-1\right)^3\left(x^2+1\right)}dx$
1

Rewrite the fraction $\frac{8x+8}{\left(x-1\right)^3\left(x^2+1\right)}$ in $4$ simpler fractions using partial fraction decomposition

$\frac{8x+8}{\left(x-1\right)^3\left(x^2+1\right)}=\frac{A}{\left(x-1\right)^3}+\frac{Bx+C}{x^2+1}+\frac{D}{x-1}+\frac{F}{\left(x-1\right)^{2}}$
2

Find the values of the unknown coefficients. The first step is to multiply both sides of the equation by $\left(x-1\right)^3\left(x^2+1\right)$

$8x+8=\left(x-1\right)^3\left(x^2+1\right)\left(\frac{A}{\left(x-1\right)^3}+\frac{Bx+C}{x^2+1}+\frac{D}{x-1}+\frac{F}{\left(x-1\right)^{2}}\right)$

Unlock this step-by-step solution!

Answer

$4arctan\left(x\right)+\frac{4}{x-1}+\frac{-4}{\left(x-1\right)^{2}}+C_0$