Integrating e^(2t)(25sint+20cost)dt using Integration by Parts

[mshiddensecret]

Homework Statement

Integrate: (e^(2t))(25sint+20cost)dt

Homework Equations

Integration by parts twice

The Attempt at a Solution

I don't know what to set for u and v.

I ended up wolfram alpha it but I want to know how to get there.

The solution is:

e^(2t)(14sint+3cost)=C

 

[Mark44]

Homework Statement

Integrate: (e^(2t))(25sint+20cost)dt

Homework Equations

Integration by parts twice

The Attempt at a Solution

I don't know what to set for u and v.

I ended up wolfram alpha it but I want to know how to get there.

The solution is:

e^(2t)(14sint+3cost)=C

You could split the integral into two parts and work each one separately. I would start off with u₁ = 25sin(t) for the first integral and u₂ = 20cos(t) for the second one. Do similar substitutions the second time you apply integration by parts.

 

[Mark44]

e^(2t)(14sint+3cost)=C

Should be + C, right?