∫ xⁿ dx = xn + 1/(n + 1) + c where n is any constant except 0 and -1.
Apply that rule to get:
∫ 5x dx
= 5 ∫ x dx [Factor out the constant]
= 5 ∫ x1 dx [Make note of the exponent for x]
= 5x1 + 1/(1 + 1) + c
= (5/2)x2 + c
The antiderivative of a function which is equal to 0 everywhere is a function equal to 0 everywhere.
The fundamental theorum of calculus states that a definite integral from a to b is equivalent to the antiderivative's expression of b minus the antiderivative expression of a.
-e-x + C.
-1
You can't, unless it's an initial value problem. If f(x) is an antiderivative to g(x), then so is f(x) + c, for any c at all.
The antiderivative of 2x is x2.
The antiderivative of a function which is equal to 0 everywhere is a function equal to 0 everywhere.
Using u-substitution (where u = sinx), you'll find the antiderivative to be 0.5*sin2x + C.
I assume you mean -10x^4? In that case, antiderivative would be to add one to the exponent, then divide by the exponent. So -10x^5, then divide by 5. So the antiderivative is -2x^5.
Antiderivative of x/-1 = -1(x^2)/2 + C = (-1/2)(x^2) + C Wolfram says antiderivative of x^-1 is log(x) + C
By antiderivative do you mean integral? If yes, integral x^1 dx= (x^2)/2
The fundamental theorum of calculus states that a definite integral from a to b is equivalent to the antiderivative's expression of b minus the antiderivative expression of a.
(that weird integral or antiderivative sign) x^(-6/5) dx =-5*x^(-1/5)
-e-x + C.
It is -exp (-x) + C.
X(logX-1) + C
An antidifferentiation is a process of calculating the antiderivative in calculus.