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# C4 Integration Watch

1. So I've had a sheet of 50 integration questions to do and several on the sheet have so far stumped me.

Any help would be appreciated thanks!

9) Sinxcos^(4)x

13) Sin^(2)2x

18) x/9x^2 + 1

24) cot^(2)3x

31) (x+1)^2/x^2+1.
I used division to work out it was the integral of 1 +(2x/x^2+1) Then how do i progress further?
2. (Original post by Henry.Lister)
So I've had a sheet of 50 integration questions to do and several on the sheet have so far stumped me.

Any help would be appreciated thanks!

9) Sinxcos^(4)x

13) Sin^(2)2x

18) x/9x^2 + 1

24) cot^(2)3x

31) (x+1)^2/x^2+1.
I used division to work out it was the integral of 1 +(2x/x^2+1) Then how do i progress further?
For many of them, you have to consider the chain rule in reverse (when you have a function multiplied by it's differential). Others involve natural logs. Does this help?
3. Hmm i recognise where you're coming from but I'm weary about knowing exactly how to do it.

Mind showing me one? Thanks
4. (Original post by Henry.Lister)
Hmm i recognise where you're coming from but I'm weary about knowing exactly how to do it.

Mind showing me one? Thanks
For 9), consider the differential of cos^(5)x.

For 18), consider the differential of ln(9x^2 +1)
5. (Original post by Henry.Lister)
So I've had a sheet of 50 integration questions to do and several on the sheet have so far stumped me.

Any help would be appreciated thanks!

9) Sinxcos^(4)x

13) Sin^(2)2x

18) x/9x^2 + 1

24) cot^(2)3x

31) (x+1)^2/x^2+1.
I used division to work out it was the integral of 1 +(2x/x^2+1) Then how do i progress further?
For 9)
Use u=cosx substitution
du/dx=-sinx -> -sinx dx =du
or use directly the rule of

that is

for 13)
Use the identity of

and
when the primitive function for f(x) is F(x)+C
then the primitive function for f(ax+b) is F(ax+b)/a +C

for 18)

For this quesion

But you can use substitution of t=9x^2+1
then dt=18x dx -> x dx =1/18 dt

for 24)

And as you know

for 31)
see 18
6. (Original post by ztibor)
x
You're not supposed to give solutions on these forums, but to help the OP reach the answer themselves
7. 9 makes sense now thanks. I'll look through 18 next.
8. Ztibor thanks, I'll look through those calculations shortly
9. I think I've managed to complete them all except I'm unsure about 13.

I tried changing the integral of sin^22x into (1-cos4x)/2 using cos2x=1-2sin^2x

I then integrated that to get 1/2x-1/4sin4x+c.
10. (Original post by Henry.Lister)
I think I've managed to complete them all except I'm unsure about 13.

I tried changing the integral of sin^22x into (1-cos4x)/2 using cos2x=1-2sin^2x

I then integrated that to get 1/2x-1/4sin4x+c.
This is the correct method - but you've made a small slip up in the solution.
Spoiler:
Show
Reverse chain rule on -cos4x.

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