Omniscience
\[\int tanxdx\]
integration by parts
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Omniscience
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i integrate it twice; but i dont know why it failed
irkiz
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separate them into tanx and dx
Omniscience
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i did\[(tanx)(x) - \int\limits xsec^{2}dx \]
hartnn
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integral sin x /cos x
put t= cos x
Omniscience
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i know..but i want to do it by parts
mayankdevnani
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- ln |cos x| + C
proof
int tan x dx = int sinx/cos x
set
u=cosx
then we find
du=-sinx dx
substitute du=-sin x, u=cos x
int sinx/cos x= - int of (-1) sin x dx / cosx
=- int of du/u
Solve the integral
= - ln |u| + C
substitute back u=cos x
= - ln |cos x| + C
mayankdevnani
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ok @Omniscience
Omniscience
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i know u-sub
i want to do it by parts
mayankdevnani
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i think it will help you!!!
Omniscience
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that's \(xtanx\)
mayankdevnani
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oh!!! sorry
irkiz
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maybe you could try converting tan x to sinx/cosx. then integrate sinxsecx by parts?
Omniscience
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ok i will try it
irkiz
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wait. is the ans ln|secx|?
Omniscience
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-ln(cosx)
irkiz
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looks the same lol
irkiz
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sec x is (cosx)^-1 bring the -1 to the front
irkiz
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yup thats the answer
Omniscience
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ok thanks