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6855227 No.6855227 [Reply] [Original]

I am having a hard time trying to find the integral of x csc^2(6x)dx using integration by parts where I chose f(x) = x and g(x) = csc^2(6x). My answer was way off I got x csc^2(6x) + 1/6 cot(6x) + c. Any tips?

>> No.6855241

>>6855227
Just u+c it?

I don't get it

>> No.6855250

switch em and see what happens

>> No.6855329

>>6855227
I don't see what the issue is here. Make sure that when doing it by parts you take the derivative of your f(x) and integrate g(x). That way you get rid of the x and are left with a trig function which you can integrate.

>> No.6855354

OP here, my issue is that when I integrate csc^2(6x), that is because this in itself needs a U substitution. So I picked my U = csc(6x) but then my DU = -6 cot(6x) * csc(6x) and I feel that is a little much so either I am choosing the wrong U or I need to integrate csc^2(6x) in some other manner.

>> No.6855379

>>6855354
it's just the power rule

>> No.6855385

>>6855354
I feel you are making this a little more complex than it needs to be. To me it sounds like you aren't familiar with the first derivatives of trig functions. Here is a hint to you. Take the 6 basic trig functions (Sin[x], Cos[x], Tan[x], Csc[x], Sec[x] and Cot[x]). Differentiate them once. Do any of them yield a Csc[x]^2. If they do then, with a little reworking, you can get the integral of Csc[6x]^2 directly. Does this make sense?

>> No.6855392

>>6855354
What's the derivative of cot?

>> No.6855427

>>6855392
The derivative of 1/tan

>> No.6855592

>>6855385
Thanks man much appreciated