(5.4 / k) cos(kt)
Integral of [1/(sin x cos x) dx] (substitute sin2 x + cos2 x for 1)= Integral of [(sin2 x + cos2 x)/(sin x cos x) dx]= Integral of [sin2 x/(sin x cos x) dx] + Integral of [cos2 x/(sin x cos x) dx]= Integral of (sin x/cos x dx) + Integral of (cos x/sin x dx)= Integral of tan x dx + Integral of cot x dx= ln |sec x| + ln |sin x| + C
-cos(x) + constant
The Integral diverges. It has singularities whenever sin(x)+cos(x)=0. Singularities do not necessarily imply that the integral goes to infinity, but that is the case here, since the indefinite integral is x/2 + 1/2 Log[-Cos[x] - Sin[x]]. Obviously this diverges when evaluated at zero and 2pi.
.5(x-sin(x)cos(x))+c
e-KT
sin integral is -cos This is so because the derivative of cos x = -sin x
Integral of [1/(sin x cos x) dx] (substitute sin2 x + cos2 x for 1)= Integral of [(sin2 x + cos2 x)/(sin x cos x) dx]= Integral of [sin2 x/(sin x cos x) dx] + Integral of [cos2 x/(sin x cos x) dx]= Integral of (sin x/cos x dx) + Integral of (cos x/sin x dx)= Integral of tan x dx + Integral of cot x dx= ln |sec x| + ln |sin x| + C
-cos x + Constant
sin2x + c
The integral of cosine cubed is sinx- 1/3 sin cubed x + c
The indefinite integral of sin 2x is -cos 2x / 2 + C, where C is any constant.
if you are studying a (simple) wave described by: x = A sin(kt) then A = amplitude
(1/8)(x-sin 4x)
-cos(x) + constant
- cos(1 - X) + C
∫ cos(x) dx = -sin(x) + C
The integral of x cos(x) dx is cos(x) + x sin(x) + C