# Calculus Problem Help Integral of (secx)^3 dx

1. Oct 4, 2004

### CinderBlockFist

Hi all, I am stuck on this trig integral problem. The answer is provided in the book, but I do not know how to get it. The problem is this:

Integral of (secX)^3 dx

it says first use integration by parts:

u = sec x du = sec x tan x dx

dv = (secx)^2 dx v = tan x

uv - integral (v du) = sex x tan x - integral sec x((secx)^2-1) dx

Then it says secx tanx - integral (sec x)^3 dx + integral sec x dx

Now there is another (sec x)^3 like in the original problem, after this step they just provide the answer, but how ?

The answer is 1/2(secxtanx + ln |secx+tanx|) + C

2. Oct 4, 2004

### arildno

Let
$$I=\int\frac{1}{\cos^{3}x}dx$$
Hence, you have shown:
$$I=sec(x)tan(x)-I+\int\frac{1}{\cos{x}}dx$$
Can you take it from there?

3. Oct 4, 2004

### CinderBlockFist

hmm, let me try, thats diff. method from the book but it looks easier, brb. thx.