Question

For \(n\ne -1\), which is the correct integral of \(x^n\)?

Options

• \[\int x^n\,dx=nx^{n-1}+\mathrm{C}\]

• \[\int x^n\,dx=\frac{x^n}{n}+\mathrm{C}\]

• \[\int x^n\,dx=\frac{x^{n-1}}{n-1}+\mathrm{C}\]

• \[\int x^n\,dx=\frac{x^{n+1}}{n+1}+\mathrm{C}\]

Answer 1

The power rule increases the exponent from \(n\) to \(n+1\). It then divides by \(n+1\), so it applies when \(n\ne -1\).