Question #e2f56

1 Answer
Vishwaksen Reddy V. ยท NickTheTurtle
Apr 6, 2017

tan(x/2)+C

Explanation:

cos^2(x/2) = (1+cos(x))/2
So 1+cos(x) = 2cos^2(x/2) and 1/(1+cos x) =1/2sec^2(x/2)
int\ 1/2sec^2(x/2)\ dx = 1/2int\ sec^2(x/2)\ dx

Substituting u=x/2 and du=dx/2, we get 1/2int\ 2sec^2(u)\ du=tan(u)+C=tan(x/2)+C

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