What is the antiderivative of $secx$ ?

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Answer 1 · 2015-06-22T04:48:54

To find the antiderivative (or integral), there is a trick to this.

$intsecxdx$

You can multiply by $(secx + tanx)/(secx + tanx)$ .

$= int(secx(secx + tanx))/(secx + tanx)dx$

$= int(sec^2x + secxtanx)/(secx + tanx)dx$

Now if you let:
$u = secx + tanx$
$du = secxtanx + sec^2xdx$

then you get:

$= int1/udu$

$= ln|u| + C$

$= ln|secx + tanx| + C$

What is the antiderivative of secxsecx?