∫(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.
More Answers:
Finding the Antiderivative | Integrating 1/u using Logarithmic FunctionMastering the Definite Integral | A Step-by-Step Guide for Evaluating ∫kf(u)du
Integration by Substitution | Solving the Integral of e^u with Respect to u