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\int_{1}^{2}\frac{1}{x\cdot\left(x+1\right)}dx

Integrate 1/(x(x+1)) from 1 to 2

Answer

$0.2877$

Step-by-step explanation

Problem to solve:

$\int_{1}^{2}\frac{1}{x\cdot\left(x+1\right)}dx$
1

Rewrite the fraction $\frac{1}{x\left(x+1\right)}$ in $2$ simpler fractions using partial fraction decomposition

$\frac{1}{x\left(x+1\right)}=\frac{A}{x}+\frac{B}{x+1}$

Unlock this step-by-step solution!

Answer

$0.2877$

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$\int_{1}^{2}\frac{1}{x\cdot\left(x+1\right)}dx$

Main topic:

Integrals by partial fraction expansion

Used formulas:

4. See formulas

Time to solve it:

~ 0.59 seconds