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

Integral of (x-1)/(x(x^2+1))

Answer

$-\ln\left|x\right|-\ln\left(\frac{1}{x^2+1}\right)+arctan\left(x\right)+C_0$

Step-by-step explanation

Problem to solve:

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

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

$\frac{x-1}{x\left(x^2+1\right)}=\frac{A}{x}+\frac{Bx+C}{x^2+1}$

Unlock this step-by-step solution!

Answer

$-\ln\left|x\right|-\ln\left(\frac{1}{x^2+1}\right)+arctan\left(x\right)+C_0$
$\int\frac{x-1}{x\cdot \left(x^2+1\right)}dx$

Main topic:

Integration by trigonometric substitution

Time to solve it:

~ 1.17 seconds