Evaluate the following integrals : ∫(5x^4+12x^3+7x^2)/(x^2+x) dx ​

Question

Evaluate the following integrals :

\(\int\frac{5x^4+12x^3+7x^2}{x^2+x}\) dx

Answer 1

Given :

\(\int\frac{5x^4+12x^3+7x^2}{x^2+x}\) dx

Now,

Spilt 12x³ into 7x³ and 5x³

\(\int\frac{5x^4+7x^3+5x^3+7x^2}{x^2+x}\) dx

Now common 5x³ from two elements 7x from other two elements,