Question

Integration of (sin(x) + Cos(x)) e^x​

Answer 1

Question:

$\int (sin(x)+cos(x))e^x$

Answer:

$e^x(sinx)$

Explanation:

$\sf \int (sin(x)+cos(x))e^x \\\\\sf \int e^x(sin~x+cos~x) ~dx \\\\\sf \mapsto \int e^x ~sinx~dx+ \int e^x ~cosx~dx \\\\\sf \mapsto e^x(sinx)- \int e^x~cosx~dx+ \int e^x~cosx~dx\\\\\sf \mapsto e^x(sinx)- \cancel{\int e^x~cosx~dx} + \cancel{\int e^x~cosx~dx} \\\\\sf \mapsto e^x(sinx) +c$