## Integrating Fractions – using the natrual logarithm – Example tan(x)

From result found be differentiating the natural logarithm,

for some function f(x),

and the fundamental theorem of calculus we cay say that

where c is the integration constant

### Simple Example

The most basic example of this is the integration of 1/x,

### More complex example: Integration of tan(x)

A slightly more complicated example of this is the integration of tan(x). To do this we must remember that and notice that . This means that -tan(x) is of the form as required. Using this we can get

### Trick for using this identity

Sometimes we get integrals that are almost in this form but not exactly, eg) , however to solve these we can often factorise a constant so that it is in the required form. In this example we can take out a 2 so we get

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Categories: calculus
differentiation, integration, logarithm, tan(x)

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