Let z = ∫(e^sin(t)dt) from x to y

Question

a = x
b = y

I tried thinking about it like a chain rule but even then i'm a little unsure.

I know dz/dt = e^sin(t). Can you please point me in the right direction if i'm supposed to use the chain rule.

Answer 1

Don't know if you really meant
∫sin(t)e^t dt
If that's the case, try differentiate using the chain rule,
sin(t)e^t
and
cos(t)e^t

You should be able to figure out the integral from the results.

The original integral you posted does not seem to have an analytic solution. A series solution is (almost always) available but does not fit your bill.

Answer 2

uh no i meant what i typed which is e^(sin(t))

Answer 3

In that case, I fear there is no solution using elementary functions.

who posed such a problem? It's solvable numerically, using a Taylor series, but not symbolically.