# Some-what fancy trig inegral

1. May 14, 2007

### Rasine

find the integral of (cosx)^2(tanx)^3

so first of all i rewrote tan to be (sinx)^3/(cosx)^3 so that i could cancle out the (cosx)^2 on top

and now i have the integral of (1/cosx)(sinx)^3

i rewrote that to be (tanx)(sinx)^2...and now i am stuck

i don't know of any IDs that could make the integral simplier...i am open to suggestions

2. May 14, 2007

### neutrino

$$\frac{\sin^3{x}}{\cos{x}} = \frac{\sin^2{x}sin{x}}{\cos{x}}$$

3. May 14, 2007

### Rasine

right...so sinx/cosx would be tanx and that would it it (sinx)^2(tanx).....right?

4. May 14, 2007

### neutrino

No. sin^2 would be 1-cos^2

5. May 14, 2007

### Rasine

ok let me try that

6. May 14, 2007

### Rasine

now i am getting the integral of tanx-sinxcosx

i know how to integrate sinxcosx but not tanx

7. May 14, 2007

### neutrino

That's strange...

tanx is just sinxcosx, except that the cosx is placed in the denominator.

8. May 14, 2007

### Rasine

oohhh ok...let me try it