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# Find the integral $\int\frac{-x^2+8x^2-9x+2}{\left(x^2+1\right)\left(x-3\right)^2}dx$

## Step-by-step Solution

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### Videos

$\frac{7}{50}\arctan\left(x\right)-\frac{51}{100}\ln\left(x^2+1\right)+\frac{-19}{5\left(x-3\right)}+\frac{51}{50}\ln\left(x-3\right)+C_0$
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## Step-by-step Solution

Problem to solve:

$\int\:\frac{-x^2+8x^2-9x+2}{\left(x^2+1\right)\left(x-3\right)^2}dx$

Specify the solving method

1

Combining like terms $-x^2$ and $8x^2$

$\int\frac{7x^2-9x+2}{\left(x^2+1\right)\left(x-3\right)^2}dx$

Learn how to solve integrals by partial fraction expansion problems step by step online.

$\int\frac{7x^2-9x+2}{\left(x^2+1\right)\left(x-3\right)^2}dx$

Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((-x^2+8x^2-9x+2)/((x^2+1)(x-3)^2))dx. Combining like terms -x^2 and 8x^2. Rewrite the fraction \frac{7x^2-9x+2}{\left(x^2+1\right)\left(x-3\right)^2} in 3 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C, D. The first step is to multiply both sides of the equation from the previous step by \left(x^2+1\right)\left(x-3\right)^2. Multiplying polynomials.

$\frac{7}{50}\arctan\left(x\right)-\frac{51}{100}\ln\left(x^2+1\right)+\frac{-19}{5\left(x-3\right)}+\frac{51}{50}\ln\left(x-3\right)+C_0$
SnapXam A2

### beta Got another answer? Verify it!

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

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

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

$\int\:\frac{-x^2+8x^2-9x+2}{\left(x^2+1\right)\left(x-3\right)^2}dx$

### Main topic:

Integrals by Partial Fraction expansion

~ 0.32 s