Recent content by crm08

Homework Statement \int\frac{dx}{9x^{2}+1} Homework Equations \frac{d}{dx}(arctan(x)) = \frac{1}{1+x^{2}} The Attempt at a Solution The other problems in this homework set all use the substitution rule but I can't find anything that would simplify the problem, my other guess...

Dick, thanks for the link, I forgot about that reduction formula.

My prof covered this whole chapter today and only introduced two "cases" that can be identified for solving these problems, each case having two methods which are chosen by looking at the even or odd powers. case 1: integral[((cosx)^m)*(sinx)^n))dx] - or - case 2...

Homework Statement \int^{\pi}_{0}(cos(x))^{6}dx Homework Equations * Half-Angle => (cos(x))^{2} = (1/2)(1 + cos(2x)) The Attempt at a Solution We just started this chapter today and during lecture the only example of this form (even powers/cosine) was (cos(x))^{2}, which only...

ok got it, thank you

Homework Statement \int(\frac{x}{\sqrt{1-x^{2}}})dx Homework Equations The Attempt at a Solution My calculator tells me that the answer should be -sqrt(1-x^2) but if I pick u = sqrt(1-x^2), then dx = (sqrt(1-x^2)*du)/x, which leaves me with -integral((sqrt(1-x^2)/u)du), the...

Ok nevermind I got it now, I was working towards an answer to this problem that my 89 gave me but I typed it in wrong, I see how to to it now, the answer being: x*arcsin(x) + sqrt(1-x^2) Thanks for your help

Yes, the problem is asking for the integral of arcsin(x), and also yes, that is the formula we are using, my "u's" and "v's" look a lot alike sometimes so I replaced them with f(x) and g(x), sorry about the confusion

Homework Statement \int(sin(x)^{-1}), dx Homework Equations *By Parts Formula: f(x)g(x) - \int(g(x) f'(x)) dx Also for d/dx sin(x)^{-1} I used 1/sqrt(1-x^{2}) The Attempt at a Solution Just started learning this method, I tried letting f(x) = sin(x)^{-1} and g(x) = dx but nothing really...

sorry never mind, its supposed to be the ln(a) not x

Homework Statement \int10^{t}dt t = [1,2] Homework Equations I know that \int(a^{x})dx = \frac{(a^x)}{ln(x)} + C and x\neq 1 The Attempt at a Solution I could do this problem as indefinate, but since the restraints include a "1", I can't plug it into the the integral because...

ok I'm getting (1/y) * dy/dx = (ln(x))*(1/sin(x))*(cos(x)) + (ln(sin(x))*(1/x) = y*[(ln(x))*(tan(x)) + ((ln(sin(x))) / x)] am I getting any closer?

Homework Statement The problem asks to graph tangent lines to the given function y = (ln(x)/x, and gives the points (1,0) and (e, 1/e) Homework Equations The Attempt at a Solution I got the answer by taking the derivative and finding the slope, and at the point (e,1/e) the...

never mind I went back to an old book, I think I got it now, thanks for the help

Oh I gotcha, so now use: d/dx (e^g(x)) = e^g(x) * g'(x), where g(x) = (sin(x))(ln(x)), and use product rule for g'(x) I think I'm on the right track