2. Integration: The Basic Logarithmic Form
by M. Bourne
The general power formula that we saw in Section 1 is valid for all values of n except n = -1. We take the opposite of the derivative of the logarithmic function to solve such cases:
The 
(absolute value) signs around
the u are necessary since the log of a negative number is
not defined.
We can also write the formula as:
In words, this means that if we have the derivative of a function in the numerator (top) of a fraction, and the function in the denominator (bottom) of the fraction, then the integral of the fraction will be the natural logarithm of the function.
Example 1: 
Example 2: 
Example 3: 
Example 4:
The equation
comes from considering a force proportional to the velocity of an object moving down an inclined plane. Find the velocity, v, as a function of time, t, if the object starts from rest.
Exercises
Integrate each of the given functions:
1. 
2. 
First, the LiveMath solution to this problem.
3. The electric power p developed in a certain resistor is given by
where t is the time. Express p as a function of t.
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