# Step-by-step Solution

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## Step-by-step Solution

Problem to solve:

$\int\frac{5x^2+14x+10}{\left(x+2\right)\left(x+1\right)^2}dx$

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$\frac{5x^2+14x+10}{\left(x+2\right)\left(x+1\right)^2}=\frac{A}{x+2}+\frac{B}{\left(x+1\right)^2}+\frac{C}{x+1}$

Learn how to solve problems step by step online. Find the integral int((5x^2+14x+10)/((x+2)(x+1)^2))dx. Rewrite the fraction \frac{5x^2+14x+10}{\left(x+2\right)\left(x+1\right)^2} in 3 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C. The first step is to multiply both sides of the equation from the previous step by \left(x+2\right)\left(x+1\right)^2. Multiplying polynomials. Simplifying.

## Final Answer

$2\ln\left(x+2\right)+\frac{-1}{x+1}+3\ln\left(x+1\right)+C_0$
SnapXam A2
Answer Assistant

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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