Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/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

# Integral of (14x+10+5x^2)/((x+2)(x+1)^2)

### Videos

$\frac{-29}{1+x}+58\ln\left|2+x\right|-53\ln\left|1+x\right|+C_0$

## Step-by-step explanation

Problem

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

Use the complete the square method to factor the trinomial of the form $ax^2+bx+c$. Take common factor $a$ ($5$) to all terms

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

$\frac{-29}{1+x}+58\ln\left|2+x\right|-53\ln\left|1+x\right|+C_0$
$\int\frac{5x^2+14x+10}{\left(x+2\right)\left(x+1\right)^2}dx$