Question

Evaluate : $\int \left(\frac{3x^4-5x^3+4x^2-x+2}{x^3}\right)dx$

Answer 1

We have,

$I=\int \left(\frac{3x^4-5x^3+4x^2-x+2}{x^3}\right)dx$

$I=\int (3x-5+\frac{4}{x}-\frac{1}{x^2}+\frac{2}{x^3})dx$

$I=(3\frac{x^2}{2}-5x+4\ln x-\left(\frac{-1}{x}\right)+\left(\frac{-2}{2x^2}\right))+C$

$I=\frac{3x^2}{2}-5x+4\ln x+\frac{1}{x}-\frac{1}{x^2}+C$

Hence, this is the answer.