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Help with following integral

Mathematics
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\[\int\limits_{0}^{\pi/2} e ^{sint}cost dt\]
sin t* I can't seem to figure out what to use. everytime I get e I get lost x.x
use integral by u-sub let u = sint du = cost dt

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Other answers:

but then I get stuck with \[e ^{u}\] wouldn't that require integration by part?
just still it self int e^u = e^u
Oh only e^2u would require by part? ( question by curiosity)
e^u not e^2u now, subtitute back that u = sint so, it is [e^(sint)]
Thank you :)
the rest is calculation difference of limits, can u ? you're welcome :)
Yeah I can I get confuse with e. I know sometimes it requires integration by part but this one was a simple case. Thanks a lot though helped me understand a bit more!
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that's the last answer

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