∫ tahh(x) dx = ln(cosh(x)) + C
C is the constant of integration.
∫ sinh(x) dx = cosh(x) + C C is the constant of integration.
∫ cosh(x) dx = sinh(x) + C C is the constant of integration.
∫ coth(x) dx = ln(sinh(x))+ C C is the constant of integration.
∫ tan(x) dx = -ln(cos(x)) + C C is the constant of integration.
∫ 1/sinh2(x) dx = -cotanh + C C is the constant of integration.
∫ 1/cosh2(x) dx = tanh(x) + C C is the constant of integration.
∫ 1/sinh(x) dx = ln(tanh(x/2)) + C C is the constant of integration.
The integral of X 4Y X 8Y 2 With respect to X is 2ln(10/9).
if you are integrating with respect to x, the indefinite integral of 1 is just x
tanh is the hyperbolic tangent and it is computed as sinh(x)/cosh(x) = [exp(x)-exp(-x)]/[exp(x)+exp(-x)] and there are other ways of computing it, including infinite series.
d/dx ∫ f(x) dx = f(x)
With respect to x, this integral is (-15/2) cos2x + C.