Question

evaluate the integral e^x sin(1+e^x)dx

Answer 1

∫ (e^x) sin(e^x) dx =
note that you have both the sine argument and its derivative,
thus let e^x = u
then, differentiate both sides, yielding:
d(e^x) = du →
(e^x) dx = du
then, substituting, you get:
∫ (e^x) sin(e^x) dx =
∫ sin(e^x) (e^x) dx =
∫ sin(u) du = - cos(u) + c
finally, substituting back u = (e^x):

∫ (e^x) sin(e^x) dx = - cos(e^x) + c

Answer 2

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Answer 3

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Answer 4

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Answer 5

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Answer 6

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