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I was trying to solve the integral of

sin(x)*cos(x)

using the substitution method, what I did was:

u=sin(x) and that yields du/dx = cos(x) and then du=cos(x)*dx

that comes to an integral of u*du, which is easy u^2 / 2 +C. substituting back gives the final answer

sin(x)^2 / 2

But, when I ran this integral in both Maple and Mathematica, I got this answer:

-cos(x)^2 / 2

Now I tried asking Maple if the two answers are the same, but it failed. I tried checking myself, using the relation sin(x)^2+cos(x)^2=1, and got to the conclusion that they don't. I don't see what I did wrong here...