Incorrect Sign In Trigonometric Integral Problem

[PhysEd]

Homework Statement

I am integrating sin(x)^3cos(x)^3, I know the technique (I hope) and I get the right equation at the end. But if I ask wolfram alpha what the integral of the equation is and enter 0 into wolfram's answer and also enter 0 into my answer, the answers come out different.

If I change the sign of my first term to negative, the answers come out the same.

So essentially I am getting:

{(cos(x))^6\over 6} - {(cos(x))^4\over 4}

While according to Wolfram Alpha I should be getting:

-{(cos(x))^6\over 6} - {(cos(x))^4\over 4}


Where am I going wrong?

The Attempt at a Solution

 

[gb7nash]

Unfortunately, you can't just plug in numbers to validate your solution. As you probably know, there are an infinite number of constants you can add to have a valid indefinite integral. If you looked on wolfram, the answer it gives has different parameters inside of the cosines. If you repeatedly apply the appropriate half angle formula, it will create more constants to throw into the overall constant. I wouldn't recommend doing this. From what I've seen though, your answer looks fine.

 

[PhysEd]

Unfortunately, you can't just plug in numbers to validate your solution. As you probably know, there are an infinite number of constants you can add to have a valid indefinite integral. If you looked on wolfram, the answer it gives has different parameters inside of the cosines. If you repeatedly apply the appropriate half angle formula, it will create more constants to throw into the overall constant. I wouldn't recommend doing this. From what I've seen though, your answer looks fine.

Ahh... of course, I forgot the C :)

Thank you!