Mastering the Power Rule for Integration: A Guide to Integrating xⁿ with Respect to x

∫ xⁿ dx

To integrate xⁿ with respect to x, where n is a constant, we can use the power rule for integration

To integrate xⁿ with respect to x, where n is a constant, we can use the power rule for integration.

The power rule states that when integrating xⁿ with respect to x, where n is any real number except -1, we add 1 to the power of x and then divide by the new power.

So, for ∫ xⁿ dx, we can use the power rule by adding 1 to the power of x, giving us xⁿ⁺¹. Then we divide by the new power, which is n⁺¹.

Therefore, the indefinite integral of xⁿ with respect to x is:

∫ xⁿ dx = (xⁿ⁺¹) / (n⁺¹) + C

Here, C represents the constant of integration.

More Answers:

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Understanding Indefinite Integrals: The Integration of Constant k with Respect to x

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