Posted by Emma on Wednesday, May 18, 2011 at 2:14am.
Please help me solve this integration problem. I don't understand how to do it. Thank you!
∫e^(2x)*sin(2x)dx

Calculus  Integration by Parts  drwls, Wednesday, May 18, 2011 at 7:44am
I do not believe you can do this in one integrationbyparts step. You must use the method twice.
Let y = 2x and dx = dy/2, to simplify the problem to
(1/2)∫e^y*sin(y)dy
Next, let e^y = u and dv = siny dy
du = e^y dy and v = cos y
(1/2)∫e^y*sin(y)dy = (1/2)*uv (1/2)∫v*du
= (1/2)[u cos y +∫e^y cosy dy]
Now you must apply integration by parts a second time on the
+∫e^y cosy dy term
This will give you an equation for
∫e^y*sin(y)dy that involves explicit functions of y.
When you are all done, substitute 2x for y
Answer This Question
Related Questions
 Calculus AP  Evaluate the integral interval from [0 to pi] t sin(3t)dt Use ...
 Calculus  I'm having trouble reversing the order of integration of ∫&#...
 Calculus AP  hi again im really need help TextBook: James Stewart:Essential ...
 Integration?  Sorry, i have a load of questions on integration... thanks for ...
 Calculus Problem  I need to find the integral of e^(2x)sin(3x) I used ...
 calculus  Use integration by parts to find ∫ 2x ex dx.
 Calculus  Use either substitution or integration by parts to evaluate the ...
 Math  Indefinite Integration  Use integration by parts to solve: I = f (x^3)(e...
 Calculus  Use integration by parts to find the given integral: ∫_9^1 (7t...
 Integration  1. [integration] (3x+7sin(x))^2 dx i tried 3 different methods of ...
More Related Questions