# Thread: [SOLVED] Integration using tan 1/2x substitution

1. ## [SOLVED] Integration using tan 1/2x substitution

Im struggling to finish this one

I = 1/( 2 + cos x) dx

using substitution t = tan1/2 x

I sub in for cos and recalcualte to give me

I = 2/(t^2 + 3) dt

I can see this is clse tot the form I = a/(t^2 + a^2) dt but can complete.

Can someone show me where I'm missing the link?

Thanks, Dan

2. Originally Posted by dojo
Im struggling to finish this one

I = 1/( 2 + cos x) dx

using substitution t = tan1/2 x

I sub in for cos and recalcualte to give me

I = 2/(t^2 + 3) dt

I can see this is clse tot the form I = a/(t^2 + a^2) dt but can complete.

Can someone show me where I'm missing the link?

Thanks, Dan
Dear Dan,

$\displaystyle \int{\frac{2}{3+t^2}}dt=2\int{\frac{dt}{(\sqrt{3}) ^2+t^2}}$

You may recall that, $\displaystyle \frac{1}{a}tan^{-1}\frac{t}{a}=\int{\frac{dt}{a^2+t^2}}$

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### integration of tan^1/2x

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