Another Trigonometric Integral Problem Help Me

[afcwestwarrior]

Homework Statement

∫sec^2 (x) * tan (x) dx

Homework Equations

sec^2 (x)= 1+tan^2(x)

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?