Use the substitution t = 1 + x² to solve ∫ x³ / (1 + x²)^½ dx between x=2 and x=0?

Answer 1

t=(1+x^2)
x^2=t-1
2xdx=dt
x^3=x^2*1/2*2xdx
substituting
1/2(t-1)dt/t^1/2
(1/2)[t^1/2dt-t^-1/2 dt]
(1/2)[2/3t^3/2-1/2t^1/2]
applying the limits
=(1/2)[2/3*2^3/2-1/2*2^1/2]
(1/2)2^1/2(4/3-1/2)

Answer 2

check the power of x terms