# Math Help - A simple problem

1. ## A simple problem

Hi folks, I stumbled on this forum in Google and it looks like a really lively and well-mainted help forum. I'm currently doing Calculus II in CEGEP and need quite a bit of help. I've been laying it off for so long and I'm so behind, but I need to start getting things together and catch up.

I'll start with a homework problem, I know you guys have a math code here (which is awesome) I'm not entirely used to it yet, so I've just posted and img of my problem (a rather simple one, but I just don't know where to begin):

We've been studying substitution method and integration by parts, I barely have a grasp on those concepts. If someone can go through this problem and lay things out for me in layman's terms, it would really help me in my first few steps.

I look forward to being a part of this forum. Mathematics is definitely something I want to drastically improve in.

Thanks/Cheers

2. Originally Posted by MerkwÜrdigeliebe
Hi folks, I stumbled on this forum in Google and it looks like a really lively and well-mainted help forum. I'm currently doing Calculus II in CEGEP and need quite a bit of help. I've been laying it off for so long and I'm so behind, but I need to start getting things together and catch up.

I'll start with a homework problem, I know you guys have a math code here (which is awesome) I'm not entirely used to it yet, so I've just posted and img of my problem (a rather simple one, but I just don't know where to begin):

We've been studying substitution method and integration by parts, I barely have a grasp on those concepts. If someone can go through this problem and lay things out for me in layman's terms, it would really help me in my first few steps.

I look forward to being a part of this forum. Mathematics is definitely something I want to drastically improve in.

Thanks/Cheers
integration by parts should work. let $u = x$ and $dv = \tan^2 x$

those are the variables usually used in the formula

3. $dv=\tan^2x\,dx$ of course.

4. thanks for the help, I don't think you guys realize that I'm incredibly oblivious to these concepts, at this point I merely repeating/following patterns, I don't actually understand what I'm doing

I followed a step by step example from Wikipedia and finished off with

x(tan^2)x + 2ln|cosx| + C

is that right?

5. Originally Posted by Krizalid
$dv=\tan^2x\,dx$ of course.
but of course, i did that to mess with you and Mr Fantastic

6. Originally Posted by MerkwÜrdigeliebe
thanks for the help, I don't think you guys realize that I'm incredibly oblivious to these concepts, at this point I merely repeating/following patterns, I don't actually understand what I'm doing

I followed a step by step example from Wikipedia and finished off with

x(tan^2)x + 2ln|cosx| + C

is that right?
um, i don't think so.

remember the formula (if you use it, i don't):

$\int u~dv = uv - \int v~du$

so that means, $\int x \tan^2 x ~dx = x \left( \int \tan^2 x~dx \right) - \int 1 \cdot \left( \int \tan^2 x ~dx \right)~dx$

so, now figure out what is $\int \tan^2 x~dx$ and plug it in

we dealt with that integral here

7. so my answer should be -2xln|cosx| + 2ln|cosx| + C

8. I believe it's x(tan x - x) + ln|cos x| + 1/2 x^2 + c

9. Yeah, this is what I ended up getting:

+ C of course...

thanks for all your help guys