Question

Integrate: ${\int }_0^{\infty }\frac{3x^2+4}{x^3+4x+1}dx$

Answer 1

$I={\int }_0^{\infty }\frac{3x^2+4}{x^3+4x1}dxlett=x^3+4x+1\Rightarrow dt=(3x^2+4)dxWhenx=0,t=1x=\infty ,t=\infty I={\int }_1^{\infty }\frac{1}{t}dt={lim}_{p\to \infty }\log \left|t\right|{|}_1^t={lim}_{p\to \infty }|log\left|t\right|-log1|=\infty Itisadivergentintegral$