t=tanx/2 substitutions for integrals

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Jingram123
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Report Thread starter 4 years ago
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Hi, I'm really stuck on some homework, it involves an integral i must solve by t-substitution. I was on the wikipedia page for this:
https://en.wikibooks.org/wiki/Calcul...ent_Half_Angle
But i can't for the life of me work out how they substituted the dx in this part:


This of course comes from:


and I understand therefore why sinx has been substituted but why is dx = 2dt/1+t^2? (shown last on the identity list) Is it just something we're expected to learn and know?
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Jingram123
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Don't worry, I worked it out, for all concerned:
t=tan(x/2)
dt/dx = (1/2)sec^2(x/2)
dt = (1/2)(1+t^2)dx
dx = 2dt/(1+t^2)
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