Integration help (any help is better than none!)

Is the first one

$\int \cos (\frac{\pi x}{2}) dx$

If so try integrating $\sin (\frac{\pi x}{2})$

1) how would integrating sin(πx/2) help with cos(πx/2)?
!

It's the πx/2 that's throwing me off.

Yeah that's the first one, although I'm going to make myself sound like an idiot here,
1) how would integrating sin(πx/2) help with cos(πx/2)?
and 2) I still don't know how I'd even go about doing that. It's the πx/2 that's throwing me off. I'm sure it's really simple once I know how, but my issue is that I don't know how to start with, haha. Urgh I feel so stupid trying to figure this out!

F

1/ (x+1)^1/2 x dx

Where does this x come from

Can you do $\int \cos (3x) dx$ as the method is the same

For question 2, another way of writing that, which i find clearer would be

1/ (x+1)^1/2 x dx

then its been put into the form of any other integral you are used to?
Hope that makes sense, i don't know how to do the integral signs etc :P

Would that be 1/3sin3x+c?

Yes that's exactly what I thought it meant, but I wasn't sure if it was a totally different problem or just another way of writing it. So let me get this right, even if the dx is a numerator to what I'm trying to integrate, it still means I'm just integrating it with respect to x, yeah?

If that's right, then you've honestly just made my day hahaha

Yes that's exactly what I thought it meant, but I wasn't sure if it was a totally different problem or just another way of writing it. So let me get this right, even if the dx is a numerator to what I'm trying to integrate, it still means I'm just integrating it with respect to x, yeah?

If that's right, then you've honestly just made my day hahaha

meant to be a multiplied sign sorry

Yes

$\displaystyle \int \dfrac{dx}{f(x)} = \displaystyle \int \dfrac{1}{f(x)} dx$

http://www.numberempire.com/texequationeditor/equationeditor.php

use that, it prevents ambiguous equations and saves time having to learning how to use latex

just copy and paste the expression

I wish I could give all a big cuddle or something to show my gratitude! I also wish I'd come here when I was first struggling for help because it would've saved a massive headache hahaha. Thanks so much everyone, you're all stars!

I wish I could give all a big cuddle or something to show my gratitude! I also wish I'd come here when I was first struggling for help because it would've saved a massive headache hahaha. Thanks so much everyone, you're all stars!