well, the second derivative is the derivative of the first derivative. so, the 2nd derivative of a function's indefinite integral is the derivative of the derivative of the function's indefinite integral. the derivative of a function's indefinite integral is the function, so the 2nd derivative of a function's indefinite integral is the derivative of the function.

An indefinite integral is a version of an integral that, unlike a definite integral, returns an expression instead of a number.

The general form of a definite integral is:

∫ba f(x) dx.

The general form of an indefinite integral is:

∫ f(x) dx.

An example of a definite integral is:

∫20 x2 dx.

An example of an indefinite integral is:

∫ x2 dx

In the definite case, the answer is 23/3 - 03/3 = 8/3.

In the indefinite case, the answer is x3/3 + C, where C is an arbitrary constant.

The antiderivative, or indefinite integral, of ex, is ex + C.

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

With respect to x, this integral is (-15/2) cos2x + C.