Evaluate the Indefinite Integral ∫cot 2x dx?
回答 (1)
2018-12-19 12:24 pm
Evaluate the Indefinite Integral ∫Cot(2x)dx?
Sol
∫Cot(2x)dx
Set y=Sin(2x)
dy/dx=dSin(2x)/dx=[dSin(2x)/(2x)]*(d2x/dx)
=2Cos(2x)dx
dy=2Cos(2x)dx
(1/2)dy=Cos(2x)dx
∫Cot(2x)dx
=(1/2)∫Cos(2x)/Sin(2x)dx
=(1/2)∫dy/y
=ln｜y｜/2+c
=ln｜Sin(2x)｜/2
Sol
∫Cot(2x)dx
Set y=Sin(2x)
dy/dx=dSin(2x)/dx=[dSin(2x)/(2x)]*(d2x/dx)
=2Cos(2x)dx
dy=2Cos(2x)dx
(1/2)dy=Cos(2x)dx
∫Cot(2x)dx
=(1/2)∫Cos(2x)/Sin(2x)dx
=(1/2)∫dy/y
=ln｜y｜/2+c
=ln｜Sin(2x)｜/2
收錄日期: 2021-04-30 22:47:22
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