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We were going over trigonometric integration in Calculus II the other day. I got the basic idea, but get lost when we're doing the u-substitution.

We had a problem like this:

[tex]\int cos^3 (x) dx[/tex]

Then we did:

[tex]\int (1 - sin^2 (x)) cos(x) dx[/tex]

Starting u-substitution:

[tex]u = sin(x)[/tex]

And

[tex]du = cos(x) dx[/tex]

So then we have:

[tex]\int (1 - u^2) du[/tex]

All reasonable so far. But then, du just kind of disappears.

[tex]u - u^3/3[/tex]

Which is

[tex]sin(x) - 1/3 sin^3 (x) + c[/tex]

I see how u-substitution works when its something simple, but I can't see how the answer here can be derived to get what was given before.

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# Trigonometric Integration and U Substitution

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