For x 2 we use the Power Rule with n=2: So for derivatives we have: And for integration we reverse the rule: The integral of xn is 1 (n+1) x(n+1) + C, for n ≠ -1. Here, C is the constant of …

Jul 23, 2025 · Power Rule of integration states that integral of a variable x raised to a power n is the same variable x raised to power (n+1) divided by the power (n+1). This is a useful relation …

The power rule of integration is used to integrate the terms that are of the form "variable raised to exponent". By the power rule, the integral of x n is (x n+1) / (n+1) + C.

The power rule for integration allows us to integrate any power of x. We'll also see how to integrate powers of x on the denominator, as well as square and cubic roots, using negative …

May 17, 2025 · Explore the fundamental power rule of integration with step-by-step derivations, practical examples, and AP Calculus problem walkthroughs.

The power rule for differentiation was derived by Isaac Newton and Gottfried Wilhelm Leibniz, each independently, for rational power functions in the mid 17th century, who both then used it …

In this Calculus 1 tutorial video, we explain the power rule for integration, and how the integral power rule is the opposite process of the power rule for differentiation in the...

The power rule for integrals allows us to find the indefinite (and later the definite) integrals of a variety of functions like polynomials, functions involving roots, and even some rational functions.

The power rule for integration along with this linearity property allow us to determine the indefinite integral involving sums of different powers of 𝑥 including polynomial, reciprocal, and radical …

The power rule is a fundamental integration technique in calculus that allows for the efficient evaluation of integrals involving variables raised to a power. It provides a straightforward …