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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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Final Answer

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

Problem to solve:

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

Choose 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.

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

Unlock this full step-by-step solution!

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.

Final Answer

$\frac{7}{50}\arctan\left(x\right)-\frac{51}{100}\ln\left(x^2+1\right)+\frac{-19}{5\left(x-3\right)}+\frac{51}{50}\ln\left(x-3\right)+C_0$
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Got another answer? Verify it!

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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

Tips on how to improve your answer:

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

Related Formulas:

5. See formulas

Time to solve it:

~ 0.36 s