Find the integral int(1/(x(x^(3/2)+1)))dx

 Exercise

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

 

Rewrite the fraction $\frac{1}{x\left(\sqrt{x^{3}}+1\right)}$ in $2$ simpler fractions using partial fraction decomposition

$\frac{1}{x}$

 

The integral of the inverse of the lineal function is given by the following formula, $\displaystyle\int\frac{1}{x}dx=\ln(x)$

$\ln\left|x\right|$

 

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

$\ln\left|x\right|+C_0$

$\ln\left|x\right|+C_0$

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