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Say I'm working with ∫ sqrt(1-cos(t)) dt

I end up with a substitution of u = 1-cos(t) and dt = du/sin(t)

sub back in: ∫ sqrt(u) / sin(t) du

Still got a t in there ... hrrmmm

So I go to wolfram alpha for some inspiration and 'show steps':

http://www.wolframalpha.com/input/?i=integrate++sqrt(1-cos(t))

After some bashing about I see what they are doing is valid - but have no idea how to go aboutspottingwhat they have done in between the substitution and ending up with an integral only in terms of u.

I need a little sub-'show-working' section - anyone care to show me how the 'ah-hah, that'll work!' moment actually comes about ?

It's simple ?

regards,

N

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# Help spotting trig identities to simplify integration

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