Question

Integral of sin 2x = ?

Answer 1

Using integration by substitution together with the known integral.

∫sin(x)dx=−cos(x)+C,
we first let u=2x⇒du=2dx.
Then

∫sin(2x)dx
=(1/2)(∫sin(2x)2dx)
=(1/2)(∫sin(u)du). =(1/2)(−cos(u))+C
=−1/2(cos(2x))+C