Find the integral ln(x)(x^2-2x+3)-int(((x^3)/3-x^23x)1/x)dx

 Exercise

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

 

The integral $-\int\left(\frac{x^3}{3}-x^2+3x\right)\frac{1}{x}dx$ results in: $\frac{-x^{3}}{9}+\frac{1}{2}x^2-3x$

$\frac{-x^{3}}{9}+\frac{1}{2}x^2-3x$

 

Gather the results of all integrals

$\left(x^2-2x+3\right)\ln\left|x\right|+\frac{1}{2}x^2-3x+\frac{-x^{3}}{9}$

 

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

$\left(x^2-2x+3\right)\ln\left|x\right|+\frac{1}{2}x^2-3x+\frac{-x^{3}}{9}+C_0$

$\left(x^2-2x+3\right)\ln\left|x\right|+\frac{1}{2}x^2-3x+\frac{-x^{3}}{9}+C_0$

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