What is the antiderivative 1 x?

The solution is quite simple: the antiderivative of 1/x is ln(|x|).

What is the antiderivative of Y?

Calculus Examples Since 1y is constant with respect to x , move 1y out of the integral. The answer is the antiderivative of the function f(x)=1y f ( x ) = 1 y .

What is antiderivative of X Square?

By the Power Rule, the integral of x2 with respect to x is 13×3 1 3 x 3 . The answer is the antiderivative of the function f(x)=x2 f ( x ) = x 2 .

How do you find the antiderivative of X 1?

Thus, F(x)=ln|x| is an antiderivative of 1x. Therefore, every antiderivative of 1x is of the form ln|x|+C for some constant C and every function of the form ln|x|+C is an antiderivative of 1x.

What is the antiderivative of ln x?

The antiderivative of ln x is the integral of the natural logarithmic function and is given by x ln x – x + C, where C is the constant of integration. Mathematically, we can write the antiderivative of ln x as ∫ ln x dx = x ln x – x + C, where C is the integration constant.

What is the antiderivative of 0?

Is the Antiderivative of 0 Equal to 0 Itself? No, the antiderivative of 0 is equal to C. We know that the antiderivative is also known as integral and hence the integral of 0 is C which is written as ∫ 0 dx = C. So, the antiderivative of 0 is not equal to 0.

How do you find the antiderivative of 1?

Is the Antiderivative of 1 Equal to 1 Itself? No, the antiderivative of 1 is equal to x + C. Another name for the antiderivative is integral and hence the integral of 1 is x + C which is written as ∫ 1 dx = x + C.

What is the integral of 2x?

The integration of 2x in calculus is equal to x square plus the constant of integration which is symbolically written as ∫2x dx = x2 + C, where ∫ is the symbol of the integral, dx shows that the integration of 2x is with respect to the variable x and C is the constant of integration.

What is the antiderivative of ex?

Therefore, every antiderivative of ex is of the form ex+C for some constant C and every function of the form ex+C is an antiderivative of ex.

What is the antiderivative formula?

If F is an antiderivative of f, then ∫ f(x)dx = F(x) + c is called the (general) Indefinite Integral of f, where c is an arbitrary constant.

What is the antiderivative of 1?

x + C
Is the Antiderivative of 1 Equal to 1 Itself? No, the antiderivative of 1 is equal to x + C. Another name for the antiderivative is integral and hence the integral of 1 is x + C which is written as ∫ 1 dx = x + C.