Integral of Trig Function Watch

funkiichiicka
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#1
Report Thread starter 8 years ago
#1
Can someone please help me find the integral of:

1/(5+3cosx)

Thanks.
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around
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try a t-substitution
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funkiichiicka
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(Original post by around)
try a t-substitution
:eek:
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around
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Assuming you don't know what it is:

http://en.wikipedia.org/wiki/Tangent_half-angle_formula

Basically, you introduce a new variable t, where t=tan(x/2) in this case. You can write cos x in terms of tan (x/2), and hence in terms of t, and then just substitute normally.
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DFranklin
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Be aware that by normal A-level standards, this is a very hard question - and pretty much impossible if you've not seen the t=tan x/2 substitution before.
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funkiichiicka
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(Original post by DFranklin)
Be aware that by normal A-level standards, this is a very hard question - and pretty much impossible if you've not seen the t=tan x/2 substitution before.
Well I'm at uni so haha. And still can't do it
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DFranklin
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Have you tried the t-substitution?
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funkiichiicka
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#8
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(Original post by DFranklin)
Have you tried the t-substitution?
Yes. But I'm stuck with secs and tans and dont know what to do with them.

I've gotten to a dead end:

\displaystyle\int \dfrac{\sec^2\dfrac{\pi}{2}}{8+2  \tan^2\dfrac{\pi}{2}}
Last edited by funkiichiicka; 8 years ago
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DFranklin
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Huh? Where do the pi/2's come from? Post your full working. (You only have to go to the point after you've done the substitution).
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