Question

what is the integral of e^sec^2 x

Answer 1

Given

∫etanxsec2(x)dx

Note that sec2(x) is the derivative of tanx, thus we can use

u=tanx→du=sec2(x)dx

Since

∫eudu=eu+C

We only have to substitute u

back into our result to get

∫etanxse2(x)dx=etanx+C