There is no real significance to sine plus cosine, now sin2(x) + cos2(x) = 1 for any x, where sin2(x) means to take the sign of the number, then square that value.
- ln ((x^2)-4)
integral of e to the power -x is -e to the power -x
The integral of x cos(x) dx is cos(x) + x sin(x) + C
The integral of cot (x) dx is ln (absolute value (sin (x))) + C. Without using the absolute value, you can use the square root of the square, i.e. ln (square root (sin2x)) + C
-cosine x
∫ 1/sinh2(x) dx = -cotanh + C C is the constant of integration.
.5(x-sin(x)cos(x))+c
∫ sin(x) dx = -cos(x) + CC is the constant of integration.
∫ sinh(x) dx = cosh(x) + C C is the constant of integration.
the integral of the square-root of (x-1)2 = x2/2 - x + C
square root x
∫ cos(x)/sin2(x) dx = -cosec(x) + C C is the constant of integration.
∫ sin(x)/cos2(x) dx = sec(x) + C C is the constant of integration.
(1/8)(x-sin 4x)
∫ 1/sin2(x) dx = -cot(x) + CC is the constant of integration.
∫ 1/sin(x) dx = ln(tan(x/2)) + C C is the constant of integration.