## ∫(u^n)du

### To evaluate the integral of u raised to the power of n (where n is a constant), you can use the power rule for integration

To evaluate the integral of u raised to the power of n (where n is a constant), you can use the power rule for integration. The power rule states that the integral of x raised to the power of n with respect to x is (x^(n+1))/(n+1), where n is not equal to -1.

Applying the power rule to the integral of u raised to the power of n, we get:

∫(u^n)du = (u^(n+1))/(n+1) + C

where C represents the constant of integration.

It’s important to note that the power rule only applies when n ≠ -1. In the case when n = -1, the integral becomes:

∫(u^(-1))du

This integral represents the natural logarithm of u, so the result is:

∫(u^(-1))du = ln|u| + C

Again, C represents the constant of integration.

In both cases, after evaluating the integral, don’t forget to include the constant of integration, as it can affect the final answer.

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