I need help on the following question:

1)\(\displaystyle \int e^{x}sin(2x)dx\)

This is what i have done:

\(\displaystyle u = sin(2x) du = 2xcos(2x) dx\)

\(\displaystyle dv = e^{x}dx v = e^{x}\)

\(\displaystyle \int e^{x}sin(2x) = sin(2x)e^{x} - \int e^{x}2cos(2x)\)

\(\displaystyle =e^{x}sin(2x) - 2\int e^{x}cos(2x)\)

\(\displaystyle =e^{x}sin(2x) - 2\int cos(2x)e^{x} - \int -2e^{x}sin(2x)\)

This is where i am stuck, what should i do next??

2)\(\displaystyle \int arctan(x)dx\)

This is what i have done:

\(\displaystyle u=arctan(x) du = \frac{1}{1+x^2}dx\)

\(\displaystyle dv = dx v= x\)

\(\displaystyle \int arctan(x) dx = arctan(x)x - \int x * \frac{1}{(1+x^2))}\)

finally i get \(\displaystyle arctan(x)x - \frac{x^2}{2(1+x^2)}\)

P.S