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

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

Answer

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

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

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

Unlock this step-by-step solution!

Answer

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

Main topic:

Integrals by partial fraction expansion

Used formulas:

6. See formulas

Time to solve it:

~ 2.37 seconds