What is the integral of sin 5X cos 10X dX?

Answer 1

use product-to-sum

formula sin u cos v =

1/2 [sin(u+v)

+ sin(u-v)]

so you get

1/2 int: (sin 15x) - (sin5x) dx

split it

1/2 int: sin 15x dx

- 1/2 int: sin 5x dx

using substitution you can conclude that

1/30 int: sin u du

- 1/10 in sin w dw

(you get the fraction change when you set dx=

du

and dw)

so then

- (cos u)/30 + (cos w)/10

replace the substitution

(cos 5x)/10 - (cos 15x)/30 + Constant