Alright. I already put a lot of thought into some of these but I cannot get the right answer out or am stuck in the middle.

1) The integral, from 0 to pi/4, of ((sinx)^4)((cosx)^2)dx

My thought process has gotten to (1/16)integral(1-cos4x)dx -integral((1/8)((cosx)^2)((sin2x)^2)dx

What do i do from here? Or is there a different way to go at it?

2) Integral, from pi/4 to pi/2 of (cotx)^2 for this one, I got all the way to solving the integral, which iThinkis -.5(cotx)^2 -ln(abs value of)sinx ...

I am stuck here, since pi/2 cant go into cotangent... what do I do?

3) The integral of 1 to radical 3 of arctan(1/x)dx. I solved this several times, and I got the integral to come out as xarctan(1/x) +.5ln(x^2 +1)

However, this is wrong, because i know that the answer SHOULD be -.468. How do i get -.468?

THANK YOU! for your helP!