need help in integration - two excamples

[Roshdy]

need help in integration

what is the right substitution to make these integrals

∫ (√x)/(x^¾+1)dx


∫x² √(4-x²)dx

 

[_Eduardo_]

Re: need help in integration

∫ (√x)/(x^¾+1)dx --> x^¾ = u


∫x² √(4-x²)dx --> x = 2 sin(u) and you need apply some trigonometric identities.

 

[neils_arm_strong]

For the first integration use
x={cos(t)}^(2/3)

second is x=2sin(t)

 

[ark5230]

The following are the solutions: