Calculus Question...
 

Evaluate the indefinate integral:

S (x+2)(x-7)^1/2 dx


(note. If anyones qualified to help me, you shouldnt need to be told but... anything raised to the 1/2 is the same as sq. root. Also that s represents the integrand.)

Should I be doing a "u-substitution"? Seemed like a good idea, but I cant seem to find anything to sub u in for, that makes du the rest of the problem.

Any help would be greatly appreciated.

Are you taking the square root of everything or just the last term (x-7)? If it's just the last term, then your answer is:
If it's the square root of everything in the integral, your answer is really big and complicated and I doubt they'd be giving you that.

http://integrals.wolfram.com/ <-- Excellent website.

Edit: To the best of my knowledge, you only use the "u substition method" (which, if memory serves, gives you Integral[ u dv ] = uv - Integral[ v du ] ) if you've got a term such as e^x or sin/cos values that do not naturally recycle themselves down to 0 under differentiation.

ok... Yea, jus the last term was under the square root. Its hard to type that though. Thanks you tons by the way.

I just need to figure out how you got that answer... haha

S (x+2)(x-7)^1/2 dx

using integration by parts:

d(uv) = udv + vdu

implies that

S u*dv = uv - S v*du.

Now just figure out the variables...

u = x + 2
du = dx

v = (2/3) * (x-7)^1.5
dv = (x-7)^0.5*dx

you should be able to figure it out from that.

That looks like its a derivative formula... Im not sure you can break up a product like that.

look up "integration by parts" in the index of your textbook. you should find that formula.

Looked it up. Thanks a million man! Somehow either we never used that in class, or that was the one class I skipped. Either way, im on track now!

Thanks again.