Doing u-substitution twice (second time with w) Example where we
do substitution twice to get the integral into a reasonable form
Doing u-substitution twice (second time with w) ⇐ Use this menu
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captions if using these subtitles. - Let's see if we can take
the integral of cosine of 5x over e to the sine of 5x dx. - And
there's a crow squawking outside of my window so I'll try to
stay focused. - So let's think about whether u-substitution
might be appropriate. Your first temptation might to said, -
"Hey, maybe we let u equal sine of 5x, and if u is equal to sine
of 5x, - we have something that is pretty close to du up here."
Let's verify that. - So du could be equal to -- so du/dx
(derivative of u with respect to x), - well we just use the
chain rule. Derivative of 5x is 5, - times the derivative of
sine of 5x with respect to 5x, that's just going to be cosine of
5x. - If we want to write this in