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# Have I made any woopsies in this integration? watch

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1. integral of (u-1)/((u+1)^2+1) du

let tan s = u + 1

so

integral of (tans -2)/(tans^2(s)+1) * sec^2s ds

= integral of tans -2 ds

= -ln( cos( arctan(u+1) ) ) -u + c

is this cool beanz
2. (Original post by ogloom)
integral of (u-1)/((u+1)^2+1) du

let tan s = u + 1

so

integral of (tans -2)/(tans^2(s)+1) * sec^2s ds

= integral of tans -2 ds

= -ln( cos( arctan(u+1) ) ) -u + c

is this cool beanz
Nearly. The second term isn't quite right though (integral of -2 ds = -2s+c, but what does s equal?)
3. It might look nicer if simplified to: (1/2)ln(u^2+2u+2)-2arctan(u+1)
4. (Original post by Mathematician!)
Nearly. The second term isn't quite right though (integral of -2 ds = -2s+c, but what does s equal?)
woops cheers

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Updated: January 19, 2010
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