Doing my review for the calculus test later this week, and I've reached a problem I'm having trouble with. Any help would be appreciated. Key: fnInt = intergral sqrt = square root abs = absolute value Evaluate the integral. fnInt[ dx / ( x sqrt((9x^2) - 7)) I'm solving using u substitution. u = 3x du = 3dx 1/3 du = dx The review says the answer is: (sqrt(7) / 21) (sec^-1) abs( (3/7) sqrt(7) x) + C I keep getting the following for my answer: (sqrt(7) / 7) (sec^-1) abs( (3/7) sqrt(7) x) + C I'm not sure where it is getting that 21 from at the bottom of the first fraction. I've tried multiple times now, but I just can't figure it out. Thanks in advance if anyone can assist me.
[Note: fiddledeedee's mathsy sibling speaking (with permission)] I haven't stepped through the entire integral, but at a guess, could you have missed a divide-by-3 -- the substitution gives dx -> du/3 on the top and x -> u/3 on the bottom (since u = 3x). Before applying a standard integral, I get to: Integral(1 / (u sqrt(u^2 - 7)), du), but I don't really have time to do the standard integral or parts tonight.
Wolfram|Alpha: Computational Knowledge Engine This website can solve anything and show you how to do it as well.
This, of course, best used when attempting the problem first. Believe me, you'll fail out pretty quickly if you use computers to do all your homework. Use it for the part you're stuck on and try to take it yourself from there.
My first instinct is to say that you're forgetting to multiply that function by the 1/3 you pulled outside the integral when you did your substitution. I would try to work on it more, but I have my own calculus and physics I need to do. :/