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# P3 Question, I'm stumped. watch

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1. Use the substitution t=tanx to show:

∫ 1/(3+5sin2x) dx = ∫ 1/(3t+1)(t+3) dt.

Cheers.
2. Well if t = tanx, dt/(secx)^2 = dx, and 1 + t^2 = (secx)^2 so dx = dt/(1+t^2)
∫ 1/(3+5sin2x) dx = ∫ 1/(3+10sinxcosx) dx and sinx cosx = tanx(cosx)^2 = tanx/(secx)^2 = t/(1+t^2)
So you have ∫ 1/(3+10sinxcosx) dx = ∫ 1/(3+10t/(1+t^2)) dt/(1+t^2)
=∫ 1/(3+3t^2+10t) dt = ∫ 1/(3t+1)(t+3) dt
3. (Original post by Bhaal85)
Use the substitution t=tanx to show:

∫ 1/(3+5sin2x) dx = ∫ 1/(3t+1)(t+3) dt.

Cheers.
INT 1/(3 + 5sin2x) dx

= INT 1/(3 + 10sinx.cosx) dx

= INT 1/(3 + 10tanx cos^2x) dx

t = tanx => dt/dx = sec^2x = 1 + t^2

INT 1/(3 + 10t(1/(1+t^2))) (1/(1 + t^2)) dt

= INT 1/(3(1+t^2) + 10t) dt

= INT 1/(3t^2 + 10t + 3) dt

= INT 1/(3t + 1)(t + 3) dt

Sorry if its hard to follow
4. Alternatively,
1/(3t+1)(t+3) = 1/(3t^2 + 10t + 3)

t = tan x
dt/dx = sec^2,
1/(3t^2 + 10t + 3) = sec^2/(3tan^2 + 10tan + 3) = 1/cos^2((3tan^2 + 10tan + 3)
= 1/(3sin^2 + 10sincos + 3cos^2) = 1/(3+5sin2x)
5. (Original post by It'sPhil...)
INT 1/(3 + 5sin2x) dx

= INT 1/(3 + 10sinx.cosx) dx

= INT 1/(3 + 10tanx cos^2x) dx

t = tanx => dt/dx = sec^2x = 1 + t^2

INT 1/(3 + 10t(1/(1+t^2))) (1/(1 + t^2)) dt

= INT 1/(3(1+t^2) + 10t) dt

= INT 1/(3t^2 + 10t + 3) dt

= INT 1/(3t + 1)(t + 3) dt

Sorry if its hard to follow
10sinx.cosx = 10tanx cos^2x How?
6. (Original post by Bhaal85)
10sinx.cosx = 10tanx cos^2x How?
10sinx.cosx = 10sinx.cosx (cosx/cosx)

= 10sinx/cosx (cosx)(cosx)
7. (Original post by It'sPhil...)
10sinx.cosx = 10sinx.cosx (cosx/cosx)

= 10sinx/cosx (cosx)(cosx)
Is that from the dx/dy part?
8. (Original post by Bhaal85)
Is that from the dx/dy part?
I haven't done anything to it ive just timesed it by 1 in a helpful form ie 1 = cosx/cosx. Then i have grouped the terms differently
9. Am I correct in assuming that this is quite a testing question?

Cheers people.
10. (Original post by Bhaal85)
Am I correct in assuming that this is quite a testing question?

Cheers people.
Yes, this would not turn up on a P3 exam; it would more likely be on P5.
11. (Original post by mikesgt2)
Yes, this would not turn up on a P3 exam; it would more likely be on P5.
Excellent, I managed to do this by myself(yay me) the other day whilst powering through the review exercise..
12. (Original post by mikesgt2)
Yes, this would not turn up on a P3 exam; it would more likely be on P5.
similar question was on one of the past papers i got form my teacher.

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