Solving Integrals with Trigonometric Functions

[chapsticks]

Homework Statement

∫ x sinx cosx dx =

Homework Equations

note that sinx cosx = (1/2) sin 2x

The Attempt at a Solution

1/2) ∫ x sin 2x dx =
(1/2) [(-1/2)x cos 2x - ∫ (-1/2)cos 2x dx] =
(1/2) [(-1/2)x cos 2x +(1/2) ∫ cos 2x dx] =
(-1/4)x cos 2x +(1/4) ∫ cos 2x dx =
(-1/4)x cos 2x +(1/4)(1/2) sin 2x + c =
(-1/4)x cos 2x +(1/8) sin 2x + c =

 

[Dick]

Homework Statement

∫ x sinx cosx dx =

Homework Equations

note that sinx cosx = (1/2) sin 2x

The Attempt at a Solution

1/2) ∫ x sin 2x dx =
(1/2) [(-1/2)x cos 2x - ∫ (-1/2)cos 2x dx] =
(1/2) [(-1/2)x cos 2x +(1/2) ∫ cos 2x dx] =
(-1/4)x cos 2x +(1/4) ∫ cos 2x dx =
(-1/4)x cos 2x +(1/4)(1/2) sin 2x + c =
(-1/4)x cos 2x +(1/8) sin 2x + c =

That looks just fine. What's the question?

 

[The_Duck]

It seems like you have an answer. So what's the issue?