y= ∫ (from 0 to lnx) sin e^t dt
i know that you do u subsitution but I am confused with the sin...
(Excuse me for using the hiatus to jump in with a diagram!)
Just in case a picture helps, and you (or anyone) do want dy/dx here...
The fundamental theorem plus chain rule implies...
... where
... is the chain rule. (Straight continuous lines differentiate downwards with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (which is the inner function of the composite, which is subject to the chain rule).
So we have...
...with one blank to fill in, and an obvious simplification.
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