Another Trigonometric Integral Problem Help Me

[afcwestwarrior]

1. The problem statement, all variables and given/known data
∫sec^2 (x) * tan (x) dx


2. Relevant equations
sec^2 (x)= 1+tan^2(x)


3. The attempt at a solution
=∫(1+tan^2 (x) or tan (x) tan (x)) tan (x) dx u=tan x, du=sec^2 dx

∫ (1+u^2) u du

= ∫u+u^2)du
= u^2/2 + u^3/3 = 1/2 tan^2(x)+ 1/3 tan^3 (x) +c

the answer in the back of the book is 1/2 tan^2(x)+c

what did i do wrong

[rock.freak667]

You didn't need to use this identity: sec2 (x)= 1+tan2(x)

u=tan x, du=sec^2 dx <-- This is an ideal start

\int tan(x) (sec^2(x) dx)



Do you see where to replace your tan(x) as u and so on now?