Question

The integral ∫(2x3-1)/(x4 + x) dx is equal to (here C is the constant of integration)

Answer 1

Given ∫(2x3-1)/(x4 + x) dx

Let I = ∫(2x³-1)/(x⁴ + x) dx

Now we have,

Divide by x²,we will get

= ∫(2x-x-²)/(x² + x-¹) dx

So now put x² + x-¹= u

On solving we will get

=> (2x – x-²)dx = du

=> I = ∫du/u

= log |u|+ C

= log |x² + x-¹ | + C

= log |(x³ + 1)/x| + C

 

 

 ∫(2x3-1)/(x4 + x) dx = log |(x³ + 1)/x| + C