A Guide to the Power Rule of Integration for Calculating Integrals of x^n

∫ x^(n) dx

The integral of x to the power of n, denoted as ∫ x^n dx, can be calculated using the power rule of integration

The integral of x to the power of n, denoted as ∫ x^n dx, can be calculated using the power rule of integration. The power rule states that when integrating a function of the form x^n, where n is any real number except -1, you can increase the exponent by 1 and divide the result by the new exponent.

So, applying the power rule to the integral of x^n, we get:

∫ x^n dx = (x^(n+1))/(n+1) + C

where C is the constant of integration.

For example, let’s say you want to integrate x^3. Using the power rule, we have:

∫ x^3 dx = (x^(3+1))/(3+1) + C
= (x^4)/4 + C

Similarly, if you want to integrate x^(-2), we have:

∫ x^(-2) dx = (x^(-2+1))/(-2+1) + C
= x^(-1)/(-1) + C
= -1/x + C

It’s important to note that the power rule does not apply when n = -1. In that case, you would use the natural logarithm function to integrate x^(-1).

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