How do you integrate $\int x {sec}^{2} x$ $int xsec^2x$ by integration by parts method?

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Answer 1 · 2016-08-01T01:51:45

$x tan x + ln | cos x | + C$ $xtanx + ln|cosx|+C$

$\int x {sec}^{2} x d x$ $int xsec^2x dx$

Integration by parts: $int f(x)g'(x) dx = f(x)g(x) - int f'(x)g(x) dx$

In this example: $f(x)=x -> f'(x) = 1$
and $g'(x)=sec^2x -> g(x) = tanx$

Therefore: $int xsec^2x dx = xtanx - int(1*tanx) dx$

$int xsec^2x dx = xtanx - int tanx dx$

$= xtanx + ln|cosx|+C$ (Standard integral)

How do you integrate int xsec^2x∫xsec2xint xsec^2x by integration by parts method?