int((x+1)/(x^3-2x^23x))dx

 Esercizio

$\int\left(\frac{x+1}{\left(x^3-2x^2+3x\right)}\right)dx$

 

Rewrite the expression $\frac{x+1}{x^3-2x^2+3x}$ inside the integral in factored form

$\int\frac{x+1}{x\left(x^2-2x+3\right)}dx$

 

Apply the formula: $\int cdx$$=cvar+C$, where $c=\frac{x+1}{x\left(x^2-2x+3\right)}$

$\frac{x+1}{x\left(x^2-2x+3\right)}x$

 

Apply the formula: $a\frac{b}{c}$$=\frac{ba}{c}$, where $a=x$, $b=x+1$ and $c=x\left(x^2-2x+3\right)$

$\frac{x+1}{x^2-2x+3}$

 

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$\frac{x+1}{x^2-2x+3}+C_0$

$\frac{x+1}{x^2-2x+3}+C_0$

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