What is $int \ tan3xsec3x \ dx$ ?

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Answer 1 · 2017-05-10T22:12:05

$int \ tan3xsec3x \ dx = 1/3sec3x + C$

A standard trigonometry differential is:

$d/dx sec x = secxtanx iff int \ secxtanx \ dx = sec x \ \ (+C)$

We can see a very close similarity with this result and out integral, so note that:

$d/dx sec ax = asecaxtanax$

for constant $a$ , Hence we have:

$int \ tan3xsec3x \ dx = 1/3sec3x + C$

What is int \ tan3xsec3x \ dx int \ tan3xsec3x \ dx?