What is the integral of $int sec^3(x)dx$ ?

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Answer 1 · 2018-08-02T19:56:17

$I=1/2[secxtanx+ln|secx+tanx|]+C$

Here,

$I=intsec^3xdx.....to(A)$

$I=intsecx(sec^2x)dx$

$I=secx color(blue)(intsec^2xdx)-int(secxtanxcolor(blue)( intsec^2xdx))dx$

$I=secx*color(blue)(tanx)-intsecxtanx*color(blue)(tanx)dx$

$I=secxtanx-intsecxtan^2xdx$

$I=secxtanx-intsecx(sec^2x-1)dx$

$I=secxtanx-intsec^3xdx+intsecxdx$

$I=secxtanx-I+color(red)(intsecxdx)....to[use,eqn.(A)]$

$I+I=secxtanx+color(red)(ln|secx+tanx|)+c$

$2I=secxtanx+ln|secx+tanx|+c$

$I=1/2[secxtanx+ln|secx+tanx|]+c/2$

$I=1/2[secxtanx+ln|secx+tanx|]+C ,where, C=c/2$

What is the integral of int sec^3(x)dxint sec^3(x)dx?