Question #54da5

1 Answer
Timber Lin
Jan 16, 2018

#1/2ln|sin(2x)|+C#

Explanation:

#intcot(2x)dx=intcos(2x)/sin(2x)dx#

you can easily change the numerator to equal the derivative of #sin(2x)#:
#=1/2int(2cos(2x))/sin(2x)dx=1/2int(d/dx(sin(2x)))/sin(2x)dx#

now use the rule for integration to #lnx#:
#int(f'(x))/f(x)dx=ln|f(x)|+C#

the integral becomes:
#=1/2*(ln|sin(2x)|+C)#
#=1/2ln|sin(2x)|+C# (1/2 times a constant is still a constant so the C doesn't change)

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