How to find antiderivative of product

[donjt81]

problem: find the anti derivative of x^5 + tan(2x)sec(2x)dx

how do you find the anti derivative of the second half of that problem tan(2x)sec(2x)

 

[d_leet]

problem: find the anti derivative of x^5 + tan(2x)sec(2x)dx

how do you find the anti derivative of the second half of that problem tan(2x)sec(2x)

Does the function y=sec(u)tan(u) look familiar at all? Perhaps as the derivative of some common elementary function?

 

[prace]

yeah, you are going to have to use u-substitution twice. I don't know if I am correct or not, but I changed everything to sin and cos before anything and manipulated it that way. I then let u = cosx and du = -sinx. For the second u-substitution, I let v=u²-1 and (1/2)dv = udu. I hope that helps and does not confuse you and more.

 

[d_leet]

yeah, you are going to have to use u-substitution twice. I don't know if I am correct or not, but I changed everything to sin and cos before anything and manipulated it that way. I then let u = cosx and du = -sinx. For the second u-substitution, I let v=u²-1 and (1/2)dv = udu. I hope that helps and does not confuse you and more.

What are you doing? What is the derivative of secant?

 

[prace]

oh yeah... I see that the deriveitive of secx = secx tanx... Hmm... looks like I went a long.. long long long way around it.. haha. Sorry about that donjt81, I hope I didn't lead you too far the wrong way. I think it comes out to the same answer. Does it? Well, I guess we can both learn a lesson, or at least myself. And that is to really look at what's in front of you with the equation before just jumping into it. I just jumped right in and started to manipulate it, when I could have just taken a minute to think about what was really there and solved it much quicker and easier.