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# Calculus question - find my error? :) watch

1. Hi The question I'm attempting is:

by expressing cosx in terms of cos(x/2), find the integral of 1/(1+cosx)

My working is this:

cosx + 1 = 2cos^2(x/2) (using the double angle formulae)

so the integral of 1/(1+cosx) = the integral of 1/(2cos^2(x/2))

therefore 2 * the integral of sec^2(x/2) = 2tan(x/2)+c

The answer to the question is supposed to be tan(x/2)+c, and I can't work out where I've gone wrong. Any help is appreciated!
2. (Original post by wamble)
Hi The question I'm attempting is:

by expressing cosx in terms of cos(x/2), find the integral of 1/(1+cosx)

My working is this:

cosx + 1 = 2cos^2(x/2) (using the double angle formulae)

so the integral of 1/(1+cosx) = the integral of 1/(2cos^2(x/2))

therefore 2 * the integral of sec^2(x/2) = 2tan(x/2)+c

The answer to the question is supposed to be tan(x/2)+c, and I can't work out where I've gone wrong. Any help is appreciated!
When you write 1/(2cos^2(x/2)) in terms of sec(x/2), try bringing the half out first, and you should end up with (sec^2(x/2))/2

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Updated: October 27, 2015
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