Evaluate the following as true or false. int tan(2x)dx=-1/2 ln|cos (2x)|+C

Harper George 2022-09-05 Answered
Evaluate the following as true or false.
tan ( 2 x ) d x = 1 2 ln | cos ( 2 x ) | + C
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Answers (1)

Emilia Boyle
Answered 2022-09-06 Author has 10 answers
Solution: True
tan ( 2 x ) d x = 1 2 ln | cos 2 x | + C
I = tan ( 2 x ) d x, substitute 2x=t, 2dx=dt
I = 1 2 tan ( t ) d t
I = 1 2 ln | sec x | + c , sec x = 1 cos x = ( cos x ) 1 , ln a m = m ln a
I = 1 2 ln | cos x | + C
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