Please check the links below.

http://www.mathportal.org/calculators/calculus/integral-calculator.php?val1=(cos(4x))/(sin(2x)%2Acos(2x))&val2=%5Cdisplaystyle%5Cint+%5Cdfrac%7B%5Ccos%5Cleft(4x%5Cright)%7D%7B%5Csin%5Cleft(2x%5Cright)%7B%5Ccdot%7D%5Ccos%5Cleft(2x%5Cright)%7D%5C%2C+%5Cmathrm+d+x&rb1=indef&val3=pi/6&val4=pi/3

http://www.mathportal.org/calculators/calculus/integral-calculator.php?val1=2%2Acot(4x)&val2=%5Cdisplaystyle%5Cint+2%7B%5Ccdot%7D%5Ccot%5Cleft(4x%5Cright)%5C%2C+%5Cmathrm+d+x&rb1=indef&val3=pi/6&val4=pi/3

How can integral of (cos(4x))/(sin(2x)*cos(2x)) has different result with integral of 2*cot(4x)?

Whereas both of them are the same, just different form.

http://www.mathportal.org/calculators/calculus/integral-calculator.php?val1=(cos(4x))/(sin(2x)%2Acos(2x))&val2=%5Cdisplaystyle%5Cint+%5Cdfrac%7B%5Ccos%5Cleft(4x%5Cright)%7D%7B%5Csin%5Cleft(2x%5Cright)%7B%5Ccdot%7D%5Ccos%5Cleft(2x%5Cright)%7D%5C%2C+%5Cmathrm+d+x&rb1=indef&val3=pi/6&val4=pi/3

http://www.mathportal.org/calculators/calculus/integral-calculator.php?val1=2%2Acot(4x)&val2=%5Cdisplaystyle%5Cint+2%7B%5Ccdot%7D%5Ccot%5Cleft(4x%5Cright)%5C%2C+%5Cmathrm+d+x&rb1=indef&val3=pi/6&val4=pi/3

How can integral of (cos(4x))/(sin(2x)*cos(2x)) has different result with integral of 2*cot(4x)?

Whereas both of them are the same, just different form.

## Comments

Thank you very much, Chen Jang.