# Integrating simple algebraic expressions

Integration is the inverse process to differentiation. Some people call it anti-differentiation.

Instead of multiplying the power at the front and subtracting one from the power, we add one to the power and then divide by the new power.

## Example

### Solution

This just means, integrate with respect to . Remember, add one to the power and divide by the new power.

The appears because when you differentiate a constant term, the answer is zero, so as we are performing 'anti-differentiation', we presume there may have been a constant term, which reduced to zero when differentiated. This is called the constant of integration.

In general:

provided

• In other words you add one to the power, divide by the new power and add the constant of integration.

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Similar rules apply to integration whereby we need to remove the brackets first as the expression has to be sums and/or differences of terms of the form .

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