The integral $\int x^n\,dx$ (for $n
eq -1$) equals

Question

Accepted Answer

D. $\dfrac{x^{n+1}}{n+1}+C$

1. The power rule for integration: increase the exponent by 1, divide by the new exponent.
2. $\int x^n\,dx=\dfrac{x^{n+1}}{n+1}+C$, valid for $n
eq -1$.
3. Check: $\dfrac{d}{dx}\left(\dfrac{x^{n+1}}{n+1}ight)=\dfrac{(n+1)x^n}{n+1}=x^n$.
_Source: NCERT Class 12 Mathematics Ch 7 "Integrals", p.289_

Answer

$n\,x^{n-1}+C$

Answer

$x^{n+1}+C$

Answer

$\dfrac{x^{n-1}}{n-1}+C$

The integral $\int x^n\,dx$ (for $n\neq -1$) equals