∫ 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.
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