What is anti derivative of x?

An antiderivative of a function f(x) is a function whose derivative is equal to f(x). That is, if F′(x)=f(x), then F(x) is an antiderivative of f(x). x33,x33+1,x33−42,x33+π. x33+c,where c is a constant.

What happens if we integrate constant?

Originally Answered: What is the integral of a constant? If you take integral with respect to , then the reslut is . Integration is inverse operation of derivation, only linear function has constant derivative. So the integral of a constant is linear function.

What are Antiderivatives used for?

An antiderivative is a function that reverses what the derivative does. One function has many antiderivatives, but they all take the form of a function plus an arbitrary constant. Antiderivatives are a key part of indefinite integrals.

What is the value of ∫1 0xxdx?

If you are willing to put bounds on your integral, it is possible to compute that ∫1 0xxdx = ∞ ∑ n = 1( − 1)n − 1 nn.

What is the indefinite integral of f(x)?

The indefinite integral of `f(x)`, denoted `int f(x)\\ dx`, is defined to be the antiderivative of `f(x)`. In other words, the derivative of `int f(x)\\ dx` is `f(x)`. Since the derivative of a constant is zero, indefinite integrals are defined only up to an arbitrary constant.

How do you express the integral xxdx as a power series?

The integral ∫ xxdx can be expressed as a double series. I asked about this series form here and the answers there show it is correct and my own answer there shows you can differentiate this back to get a power series for xx : ∫xxdx = ∞ ∑ n = 1n − 1 ∑ k = 0xnlogk(x)( − 1)1 + n + k nn − k k!

What is the derivative of ∫ f(x)dx?

In other words, the derivative of ∫ f (x)dx ∫ f ( x) d x is f (x) f ( x). Since the derivative of a constant is 0, indefinite integrals are defined only up to an arbitrary constant.