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∫ 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

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15x2/2 + C That is (2.5x2 plus any number).

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.

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

Antiderivative of x/-1 = -1(x^2)/2 + C = (-1/2)(x^2) + C Wolfram says antiderivative of x^-1 is log(x) + C

(that weird integral or antiderivative sign) x^(-6/5) dx =-5*x^(-1/5)

- 5x * - 5x = 25x2 ======

An antidifferentiation is a process of calculating the antiderivative in calculus.

It is -5*(3x + 1), no exponents are required.

It is an inverse function of a derivative, also known as an integral.

It is -exp (-x) + C.

The general formula for powers doesn't work in this case, because there will be a zero in the denominator. The antiderivative of 1/x is ln(x), that is, the natural logarithm of x.

10x - 5x + 5x = 10x

45-5x = 5x+55 -5x-5x = 55-45 -10x = 10 x = -1

5x+5x-10 10x-10 is the only answer you can get from this

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.

since the antiderivative of sinx^-1 is 1/sqrt(1-x^2), then the antiderivative of sqrt(1-x^2) is cscx^-1

The anti-derivative of any constant c, is just c*x. Thus, the antiderivative of pi is pi*x. We can verify this by taking the derivative of pi*x, which gives us pi.

For example, the derivate of x2 is 2x; then, an antiderivative of 2x is x2. That is to say, you need to find a function whose derivative is the given function. The antiderivative is also known as the indifinite integral. If you can find an antiderivative for a function, it is fairly easy to find the area under the curve of the original function - i.e., the definite integral.

An antiderivative, F, is normally defined as the indefinite integral of a function f. F is differentiable and its derivative is f.If you do not assume that f is continuous or even integrable, then your definition of antiderivative is required.

If: x = -3x+1 Then: x+3x = 1 => 4x =1 So: x = 1/4 or 0.25 ----------- I notice that the question requests a solution for g x = -3x + 1. It seems possible that parentheses around the 'x' after the 'g' have gone missing, along with a prime indicating the derivative of the function g. This being the case, we would be seeking the antiderivative of -3x + 1. The antiderivative of a sum is the sum of the antiderivatives. So we can look at -3x and +1 separately. The derivative of x2 is 2x. Therefore, the antiderivative of x is x2/2, and the antiderivative of -3x is -3x2/2. The antiderivative of 1 is x. Overall, the solution is the antiderivative -3x2/2 + x + C, where C is an arbitrary constant.

2X2+5x-12 4+5x-12 -8+5x 5x-8

25x2 + 40x + 16 = 25x2 + 20x + 20x + 16 = 5x(5x + 4) + 4(5x + 4) = (5x + 4)(5x + 4) or (5x + 4)2

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