What happens when n = −1?

When n = −1, you cannot use the power rule. Instead, ∫x⁻¹ dx = ln|x| + C (the natural logarithm of the absolute value of x).

Why is there a + C at the end?

Because differentiation of a constant gives zero, any antiderivative could have an arbitrary constant added. The + C represents this unknown constant.

Calculus

Integral: Power Rule

Formula

∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ −1)

What is Integral: Power Rule?

The power rule for integration is the reverse of the power rule for derivatives. Add 1 to the exponent, then divide by the new exponent. Add the constant of integration C.