How to Integrate (e^cost)(sin2t)dt with Substitution and Integration by Parts?

[xibalba1]

Int (e^cost)(sin2t)dt Ahhh!

Homework Statement

First make a substitution and then use integration by parts

Homework Equations

INTEGRAL OF (e^cost)(sin2t)dt

The Attempt at a Solution

the 2t is bothering me.

try subbing u=e^cost

thank you.

 

[HallsofIvy]

Homework Statement

First make a substitution and then use integration by parts

Homework Equations

INTEGRAL OF (e^cost)(sin2t)dt

The Attempt at a Solution

the 2t is bothering me.

try subbing u=e^cost

thank you.

I would not use e^cos t. I would use the trig identity, sin(2t)= 2sin(t)cos(t) so that the integral became $2\int e^{cos(t)}cos(t)sin(t)dt$ and use the substitution u= cos(t), then integration by parts.