Question

integral of
e^x (sinx +cosx)

Answer 1

integration by parts

Answer 2

or you can distribute e^x first then separate the integrals then integration by parts

Answer 3

anything works

Answer 4

\[\int e^x (sinx +cosx)dx\] Note that f(x) = sinx, f'(x) = cosx
And \[\int e^x(f(x)+f'(x))dx = e^xf(x)+C\]

Answer 5

That should be pretty easy then.

Answer 6

there's a shortcut like that? o.O :O

Answer 7

@Adhish002
\(\Huge \mathcal{\text{Welcome To OpenStudy}\ddot\smile} \)

you can also use the standard relation,
\(\\ \huge 26. \color{red}{\int e^x[f(x)+f’(x)]dx=e^xf(x)+c}\)
and figure out what f(x) is ...

Answer 8

It's about observation, in this case.

Answer 9

You can remember this,
whenever you have
\[ \int\limits\limits_{}^{} e^x (f(x) + f'(x)) dx \]
solution is \[e^x f(x) + c\]

Answer 10

so many solutions...

Answer 11

just write out the trigonometric functions in terms of complex exponentials

Answer 12

and What's the derivative of e^x(sinx+cosx) ????

Answer 13

for derivative of that, you'll need product rule, know what is it ?

Answer 14

use sage

Answer 15

use mathematica

Answer 16

wonder when wolframalpha will appear in that list

Answer 17

yes hartnn :) ty all for helping :)

Answer 18

Lol the reverse..
\[\int e^x(f(x)+f'(x))dx = e^xf(x)+C\]Then\[ e^x(f(x)+f'(x))= (e^xf(x))'\]

Answer 19

But in this case, f(x) = sinx + cosx

Answer 20

if you want us to verify your answer, post it here, we'll verify for you :)

Answer 21

i admire brave trolls who troll in front of two moderators =))

Answer 22

Solution posted as attachment