Evaluate the integral

To evaluate, apply integration by parts .

So let

and

Then, differentiate u and integrate dv.

and

Plug-in them to the formula of integration by parts. So the integral becomes:

To evaluate, apply integration by parts .

So let

and

Then, differentiate u and integrate dv.

and

Plug-in them to the formula of integration by parts. So the integral becomes:

To take the integral of (2x + 2sinx)dx, apply integration by parts again.

So let

and

Differentiate u_2 and integrate dv_2.

and

So the integral becomes:

Since the given is indefinite integral, add C.

Therefore, .