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what are the trig substiution formulas again?

like S 1/(x+x^2) = arctanx

thats wonderful and all...but my friend needs help doing this for his final tomorrow and he asked me. I haven't done this stuff in two years, and although I find it easy, I don't remember the exact formulas with symbols rather than numbers


S a/(a+x^2) = a*arctan(x/a) is that right?

Basically I'l looking for the formulas for not only tan, but sin,cos,sec,csc,cot....

i've googled and I can't find them in symbolic form...all use simple examples so I can't tell exactly where the stuff came from
 
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