# Integration problem

## Homework Statement

Compute the following antiderivative $$\int (sin^3(x))(cos^4(x)) dx$$

## 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

HallsofIvy
Homework Helper
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:
$$\int sin^3(x)cos^4(x)dx= \int sin^2(x)cos^4(x) sin(x)dx= \int (1- cos^2(x))cos^4(x) sin(x)dx[/itex] Now what substitution will make that easy? All you should do is new variable u = cos(x). You'll get integral u^4-u^6. Actually, [tex]u^6 - u^4$$ due to the negative in the derivative of $$cos(x)$$

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

fikus what do you mean, i can do a substitution straight away?
you can once you find that the derivative of your substitution appears in your original problem

HallsofIvy