# I want to know how to integrate Sin(2x)*Sin(5x)dx?

##### 1 Answer

Mar 5, 2018

#I=1/42(7sin(3x)-3sin(7x))+C#

#### Explanation:

We want to solve

#I=intsin(2x)sin(5x)dx#

Use the product identity

#sin(a)sin(b)=1/2(cos(a-b)-cos(a+b))#

With

#I=1/2int(cos(3x)-cos(7x))dx#

Which is much more comfortable to integrate

#I=1/2(1/3sin(3x)-1/7sin(7x))+C#

Or

#I=1/42(7sin(3x)-3sin(7x))+C#