Integrating sinx and x sinx cosx using sin2x identity

[Natasha1]

I have been asked to find the integral sinx cox dx and the integral x sinx cosx dx using the identity sin2x = 2sinxcosx

I don't know what to do. Can anyone help please, hints,... answers? :-)

 

[StatusX]

You can integrate sin(2x), right?

 

[Natasha1]

You can integrate sin(2x), right?

is it -2 cos x?

 

[StatusX]

Don't guess. You can check to see if the derivative of that gives you back sin(2x). It doesn't, and doing that should help you see what would.

 

[VietDao29]

As StatusX has pointed out, it's not!
Looking at your integral table (if integration is new to you, then it's best to have an integral table with you when integrating), you should see something that reads:
$$\int \sin x dx = - \cos x + C$$
Since x is a dummy variable, x can be anything, such as:
$$\int \sin u du = - \cos u + C$$
$$\int \sin \left( e ^ x \right) d \left( e ^ x \right) = - \cos \left( e ^ x \right) + C$$...
So you should use a u-substitution here. What is u? (u = ?)