# Integration problem

1. Nov 27, 2007

### tunabeast

1. The problem statement, all variables and given/known data
Compute the following antiderivative $$\int (sin^3(x))(cos^4(x)) dx$$

2. Relevant equations

3. The attempt at a solution
If this problem requires use of integration by parts i'm struggling to work out to split it up and make it manageable. Have searched countlessly for a similar example on the net but have had no luck. Thanks

2. Nov 27, 2007

### HallsofIvy

Staff Emeritus
There is a standard "method" when you have a trig function to an odd power.

Since sin(x) it to the 3rd power, take one out to use with dx, convert sin2(x) to cos:
$$\int sin^3(x)cos^4(x)dx= \int sin^2(x)cos^4(x) sin(x)dx= \int (1- cos^2(x))cos^4(x) sin(x)dx[/itex] Now what substitution will make that easy? 3. Nov 27, 2007 ### fikus All you should do is new variable u = cos(x). You'll get integral u^4-u^6. 4. Nov 27, 2007 ### colby2152 Actually, [tex]u^6 - u^4$$ due to the negative in the derivative of $$cos(x)$$

Last edited: Nov 27, 2007
5. Nov 27, 2007

### tunabeast

fikus what do you mean, i can do a substitution straight away?

6. Nov 27, 2007

### rocomath

you can once you find that the derivative of your substitution appears in your original problem

7. Nov 27, 2007

### HallsofIvy

Staff Emeritus
I believe that is what everyone as been trying to tell you!