Integral: 𝛼^(2x)cos(x)dx Solution

[Pupil]

Homework Statement

$$\int$$$$e^{2x}cos(x)dx$$

Homework Equations

The Attempt at a Solution

This isn't exactly a homework question, but it's close enough: it's from my old Calculus book (Larson), and I've been stuck on it for awhile. I just need a little hint or something. I've tried a u-substitution and haven't found anything that seems to help, and I've tried integration by parts, but nothing really simplifies--I just end up with an integral that is just as hard as before I try integration by parts. Maybe I'm using these techniques wrong or not seeing something obvious. No other 'harder' integration techniques should be needed (they come later in the book). Thanks!

 

[vela]

Try integrating by parts twice. You'll eventually end up with a term that looks like the original integral. You can collect terms, so to speak, and solve for the integral.

 

[Pupil]

Ah! I would've never thought of that. Thanks!