Question

How to integrate? Please help

`int_0^(pi/4)(3^tanx)/(1-sin^2x)dx`

Answer 1

See below.

Explanation:

`d/dx a^tanx = ln a sec^2x a^tanx`

and

`a^tanx/(1-sin^2 x) = sec^2 x a^tanx = ln a/lna sec^2x a^tanx`

so concluding

`int_0^(pi/4) a^tanx/(1-sin^2 x)dx =1/ln a (a^tan x)_0^(pi/4) = (a-1)/ln a`