Question

Integrate

Answer 1

\[\Huge \int\limits_{}^{} \sin x . e^x\]

Answer 2

You want step-wise solution or just answer?

Answer 3

I'm caught in an infinite loop using by parts

Answer 4

\[\Huge \sin x \int\limits_{}^{} e^x - \int\limits_{}^{} [\cos x \int\limits_{}^{} e^x]\]

Answer 5

\[\Huge \sin x. e^x - \int\limits\limits_{}^{} [\cos x . e^x]dx\]

Answer 6

\[\large =\sin x e^x-\int e^x\cos x\\ \large \sin x e^x -(e^x\sin x-\int e^x (-\sin x))\]
using by parts again

Answer 7

i got the basic idea of what you're gonna do,that changes to I

Answer 8

now if we let
\[\int e^x \sin x=I\]
\[I=e^x \sin x-e^x\cos x-I\]
\[I=\frac{e^x}{2}(\sin x-\cos x)\]

Answer 9

nice :O

Answer 10

previusly i made a mistake by using sin x instead of cos x

Answer 11

yeah,spotted that one

Answer 12

Ooo this is a fun integral :D

Answer 13

yeah :P

Answer 14

nice one, ty

Answer 15

+c

Answer 16

lol yeah

Answer 17

$$\sin x=\Im\{e^{ix}\}\\\int e^x\sin x\,dx=\Im\int e^xe^{ix}\,dx=\Im\int e^{(1+i)x}\,dx=\dots$$