Question

How can I Integrate (secx+tanx)^2?

Answer 1

http://www.wolframalpha.com/input/?i=integrate+%28+sec%28x%29+%2B+tan%28x%29%29^2
And hit show steps

Answer 2

=> sec^2 x + tan^2 x +2 tanx sec x
now you can integrate each term separately
integral(sec^2 x)= tanx
write tan^2 x = sec^2 x -1
and integral(sec x tanx) = sec x..

Answer 3

According to Wolfram, you get
\[
\int (\tan (x)+\sec (x))^2 \,
dx=\frac{4 \sin
\left(\frac{x}{2}\right)}{\
\cos
\left(\frac{x}{2}\right)-\sin
\left(\frac{x}{2}\right)}-x + C
\]

Answer 4

Ah! I got it! Thanks guys!