Question

Evaluate ∫x³/(1+x²)² dx

\(\frac{x^3}{(1+x^2)^2}\)dx

Answer 1

∫x³/(1+x²)² dx

Let, 

x = tan t 

Differentiating both side with respect to t,

\(\frac{dx}{dt}\) = sec²t

⇒ dx = sec²t dt

Again, 

Let cos t = z 

Differentiating both side with respect to t,

\(\frac{dx}{dt}\) = - sin t

⇒ -dz = sin t dt