What is integral of ln x?

We see that the integral of ln(x) is xln(x) – x + C.

What is integration of e 3x?

The answer is ∫e3xdx=e3x3 . So we have f(x)=e3x=g(h(x)) , where g(x)=ex and h(x)=3x . ∫e3xdx=13∫e3x⋅3dx=e3x3 . That’s it.

What is the integration of 1 log X?

Answer:1/log x) dx = t ^−1 .

What is the integral of secant X?

The integral of sec x is ln|sec x + tan x| + C. It denoted by ∫ sec x dx. This is also known as the antiderivative of sec x. We have multiple formulas for this. But the more popular formula is, ∫ sec x dx = ln |sec x + tan x| + C.

How to integrate E^X?

If you have e^ (-x), you must divide e^ (-x) by (-1), cuz (-1) is the coefficient of (-x) that’s the way you integrate when you have e^ (-3x) you must divide e^ (-3x) by (-3)… so on… or more simply, divide by the derivative of the power.

How do you find the integral?

The symbol for Integral is a stylish S. (for Sum, the idea of summing slices): After the Integral Symbol we put the function we want to find the integral of (called the Integrand), and then finish with dx to mean the slices go in the x direction (and approach zero in width).

What is the integral of 1 over X?

Answers to the question of the integral of 1 over x are all based on an implicit assumption that the upper and lower limits of the integral are both positive real numbers. If we allow more generality, we find an interesting Paradox. For instance, suppose the limits on the integral are from -A to +A where A is a real, positive number.

What is the integration of an exponential function?

Integration of Exponential Functions. Exponential functions are those of the form \\(f(x)=Ce^{x}\\) for a constant \\(C\\), and the linear shifts, inverses, quotients, of such functions. The exponential function occurs frequently in the physical sciences, so exponential functions do as well, and it can be very helpful to be able to integrate them.