Question

Integral 2 cosec 2x cotan 2x dx

Answer 1

Verified answer

Integral adalah lawan dari turunan
y = sin x => y' = cos x
y = cos x => y' = -sin x
y = tan x => y' = sec^2 x ==> diperoleh dari turunan y = (sin x)/(cos x)
y = sex x => y' = sec x tan x ==> diperoleh dr turunan y = (cos x)^-1
y = cotan x => y' = -cosec^2 x => diperoleh dr turunan y = (cos x)/(sin x)
y = cosec x => y' = -cosec x cotan x => diperoleh dr turunan y = (sin x)^-1

karena y = cosec x => y' = - cosec x cotan x
maka
∫ cosec x cotan x dx = - cosec x + C

Misal
u = 2x
du = 2 dx
∫ 2 cosec 2x cotan 2x dx
= ∫ cosec 2x . cotan 2x . 2 dx
= ∫ cosec u cotan u du
= -cosec u + C
= -cosec 2x + C