Can some help me do this C4 integration question please (Will rep) :)

Using U-Substitution I get a different answer:

You should be getting:

-1/4(e^2x + 1)^-2

Because:

Integral = e^2x . 1/u^3 where u = e^2x + 1
du = 2e^2x dx

there fore = 1/u^3 . du/2 and take out the factions

sorry, yeah thats the right answer, can you explain the last part sorry i didn't follow

You want to always split things up when working with U-Substitution.

Then you want to replace what you have with u's

so earlier we said lets make u=e^2x + 1
we then want to differentiate it so du/dx= 2e^2x
we want to replace dx for du so take dx over
du = 2e^2x dx.

Earlier we said the integral = e^2x (times by) 1/(e^2x + 1) dx
Notice, by splitting we can get that e^2x dx.
If we divide du by 2 it equals = e^2x dx
This is what we want, so swap our x's for u's
and bam, then integrate it!

thanks so much, can you integrate this as well? integrate (cos(x))/((cos(x)^2)^(3/2))

as in? :

Cos^2(x) or cos(x^2) on the denominator?

It's okay i managed to do it eventually haha thanks anyway

No problem mate! Just message me if you have any more questions and I'll see if I can help you!