1/ln(x)*e^(1/x)
if you differentiate e^(1/x), you will get ln(x)*e^(1/x). times this by 1/ln(x) and you get you original equation. Peace
Powers of e are simple to integrate. The derivative of eu equals u'eu; inversely, the antiderivative of eu equals eu/u'. Therefore, the antiderivative of e1/-x equals (e1/-x)/{d/dx[1/-x]}. The derivative of 1/-x, which can also be expressed as x-1, equals (-1)x(-1-1) = -x-2 = -1/x2.
The antiderivative of 1/x is ln(x) + C. That is, to the natural (base-e) logarithm, you can add any constant, and still have an antiderivative. For example, ln(x) + 5. These are the only antiderivatives; there are no different functions that have the same derivatives. This is valid, in general, for all antiderivatives: if you have one antiderivative of a function, all other antiderivatives are obtained by adding a constant.
int(e 3x) = (1/3)e 3x ========
if you mean e to the x power times log of x, it is e to the x divided by x
The order of operations is not clear; for example, what goes into the numerator and what goes into the denominator. Please rewrite, using appropriate parentheses. For example, if there is an addition in the denominator, put parentheses around the entire denominator.
Powers of e are simple to integrate. The derivative of eu equals u'eu; inversely, the antiderivative of eu equals eu/u'. Therefore, the antiderivative of e1/-x equals (e1/-x)/{d/dx[1/-x]}. The derivative of 1/-x, which can also be expressed as x-1, equals (-1)x(-1-1) = -x-2 = -1/x2.
The antiderivative, or indefinite integral, of ex, is ex + C.
-e-x + C.
One can use integration by parts to solve this. The answer is (x-1)e^x.
The antiderivative of 1/x is ln(x) + C. That is, to the natural (base-e) logarithm, you can add any constant, and still have an antiderivative. For example, ln(x) + 5. These are the only antiderivatives; there are no different functions that have the same derivatives. This is valid, in general, for all antiderivatives: if you have one antiderivative of a function, all other antiderivatives are obtained by adding a constant.
int(e 3x) = (1/3)e 3x ========
The integral would be 10e(1/10)x+c
Power is energy divided by time, P=E/t.
You gave no examples to choose from. Power is Energy divided by time. P = E/t In the metric system, the unit of power is the Watt. One Watt is one Joule per second, energy divided by time, 1 J/s. Power is the rate of change of energy.
if you mean e to the x power times log of x, it is e to the x divided by x
Average power equals Work divided by time. P= W/t
James E. Preston has written: 'One world divided'