Question

Evaluate:

`int(2x^3 - 1)/(x^4 + x)dx`

Answer 1

`int(2x^3 - 1)/(x^4 + x)dx`

Dividing both nominator and denominator by ‘x’ we get

Let `x^2 + 1/x = t`

`\implies (2x - 1/x^2)dx = dt`

= `int(2x - 1/x^2)/(x^2 + 1/x)dx`

= `int dt/t`

= `log_e|t| + c`

= `log_e|x^2 + 1/x| + c`