the integral is from 0 to π/4:

(1 + tanθ)^3(sec^2θ)dθ

So, here's what I did:

u = 1 + tanθ

du = sec^2θdθ

so,

(u)^3du

then, I changed the integral limits because I think I'm supposed to (not sure?)

1 + tanθ(π/4) = 2

1 + tanθ(0) = 1

so,

1/4(u)^4

then I simply plugged the new limit numbers into the equation to finish it

[1/4(2)^4] - [1/4(1)^4] = 15/4

Did I do it right?