Sexy Integral

[Dr.Moo]

integrate( X^(5/2) * (X+1) ^(1/2) dx) Upper limit 1 lower limit 0.

Anyone have a better way to do this?

I resorted to let X= (tan U)^2
dx= 2 tan U (sec U) ^2

Then converted everything to secants and used an integration table.
integral (Sec U) ^n = [(Sec U)^(n-2)]/[n-1] + [n-2]/[n-1] * integral (sec U)^ (n-2)

then convert everything back to x and put in the limits.

Anything better?

[The Jitterskull]

Wow, that made MAPLE 12 lag like fuck.

(61/192)*sqrt(2)-(5/128)*ln(3+2*sqrt(2))

Thats the answer it gave me. That must be one bitch of an integral! I will try this later tonight-- though don't count on it

[Dr.Moo]

Originally Posted by Nightside Eclipse

Wow, that made MAPLE 12 lag like fuck.

(61/192)*sqrt(2)-(5/128)*ln(3+2*sqrt(2))

Thats the answer it gave me. That must be one bitch of an integral! I will try this later tonight-- though don't count on it

Thanks for a usable answer that I can compare mine to.

[Mathematics]

http://www14.wolframalpha.com/input/?i=INTEGRATE+x^(5%2F2)+(1%2Bx)^(1%2F2)+dx

Click on show steps. It is a tricky one.