Question

integrate x^5/root 1+x^2​

Answer 1

Answer:

Hello,

Put z = (1+x^2)^1/2

then , dz = x/(1+x^2)^1/2

Also, x^4 = (z^2-1)^2

Now , I = integral (z^2-1)^2 dz

=> I = integral (z^4 +1 -2z^2)dz

=> I = (z^5)/5 + z - (2z^3)/3 +C

substituting z = (1+x^2)^1/2 we get; so, I = {(1+x^2)^5/2}/5 + (1+x^2)^1^2

- 2 {(1+x^2)^3/2}/3 +C

ans....

Thank you! !