Q: What is the integral of x to the half?

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In reimann stieltjes integral if we assume a(x) = x then it becomes reimann integral so we can say R-S integral is generalized form of reimann integral.

if you are integrating with respect to x, the indefinite integral of 1 is just x

By antiderivative do you mean integral? If yes, integral x^1 dx= (x^2)/2

integral x/(x-1) .dx = x - ln(x-1) + c where ln = natural logarithm and c = constant of integration alternatively if you meant: integral x/x - 1 .dx = c

If F(x) is a function, and F ‘(x) = f(x), then F(x) is the antiderivative (or indefinite integral) of f(x) It is the cornerstone of integral calculus and is used for areas, volumes, lengths and so much more!

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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

integral (a^x) dx = (a^x) / ln(a)

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

In reimann stieltjes integral if we assume a(x) = x then it becomes reimann integral so we can say R-S integral is generalized form of reimann integral.

if you are integrating with respect to x, the indefinite integral of 1 is just x

The integral of 2-x = 2x - (1/2)x2 + C.

The integral of arcsin(x) dx is x arcsin(x) + (1-x2)1/2 + C.

By antiderivative do you mean integral? If yes, integral x^1 dx= (x^2)/2

integral x/(x-1) .dx = x - ln(x-1) + c where ln = natural logarithm and c = constant of integration alternatively if you meant: integral x/x - 1 .dx = c

The integral of X 4Y X 8Y 2 With respect to X is 2ln(10/9).

I wasn't entirely sure what you meant, but if the problem was to find the integral of [sec(2x)-cos(x)+x^2]dx, then in order to get the answer you must follow a couple of steps:First you should separate the problem into three parts as you are allowed to with integration. So it becomes the integral of sec(2x) - the integral of cos(x) + the integral of x^2Then solve each part separatelyThe integral of sec(2x) is -(cos(2x)/2)The integral of cos(x) is sin(x)The integral of x^2 isLastly you must combine them together:-(cos(2x)/2) - sin(x) + (x^3)/3