Simple Calculus (indefinite integral)

[AryRezvani]

Homework Statement

Find the indefinite integral:
∫ Cos³2x Sin²2x dx

Homework Equations

None required

The Attempt at a Solution

Lost on where to start. If someone could just start me off.

 

[lurflurf]

either use the identity
cos³(2x)sin²(2x)=(1/16) (2 cos(2 x)-cos(6 x)-cos(10 x))
or
cos³(2x)sin²(2x)=(1/2)(sin²(2 x)-sin⁴(2 x))(sin(2x))'
and the substitution u=sin(2x)

 

[SammyS]

Homework Statement

Find the indefinite integral:
∫ Cos³2x Sin²2x dx

Homework Equations

None required

The Attempt at a Solution

Lost on where to start. If someone could just start me off.

Write cos³(2x) as cos(2x) cos²(2x)

Then use the identity,

cos²(2x)=1-sin²(2x)​

After that, a simple substitution should work fine.

 

[AryRezvani]

Write cos³(2x) as cos(2x) cos²(2x)

Then use the identity,

cos²(2x)=1-sin²(2x)​

After that, a simple substitution should work fine.

Knocked it out, thanks guys.