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## Main Question or Discussion Point

Out of curiosity there are several trig functions that can be integrated (WITHOUT the use of trig identities) using Integration by Substitution.

One particular example is this:

sin(x)cos(x) dx

Integrating this with substitution u = cos(x) works out fine.

HOWEVER integrating with substitution u = sin(x) does not.

Can someone please explain why this is, and how to distinguish what substitution to make?

One particular example is this:

sin(x)cos(x) dx

Integrating this with substitution u = cos(x) works out fine.

HOWEVER integrating with substitution u = sin(x) does not.

Can someone please explain why this is, and how to distinguish what substitution to make?