$\displaystyle\int x^n\,dx$ (for $n\neq -1$) equals:
A$x^{n+1} + C$
B$\dfrac{x^{n-1}}{n-1} + C$
C$n x^{n-1} + C$
D$\dfrac{x^{n+1}}{n+1} + C$
Answer & Solution
Correct answer: D. $\dfrac{x^{n+1}}{n+1} + C$
By the power rule for integration, ∫xⁿ dx = x^{n+1}/(n+1) + C for n ≠ −1.
Related questions
$\displaystyle\int_2^3 \dfrac{x\,dx}{x^2+1}$ equals$\displaystyle\int_0^{2a} f(x)\,dx$ equals $2\displaystyle\int_0^{a} f(x)\,dx$ precisely wIf $f(a+b-x)=f(x)$, then $\displaystyle\int_a^b x\,f(x)\,dx$ is equal to$\displaystyle\int \frac{dx}{e^{x}+e^{-x}}$ is equal toA rational function $\dfrac{P(x)}{Q(x)}$ is called proper when$\displaystyle\int_0^{\pi/4} \tan x\,dx$ equals$\displaystyle\int_0^{1} x e^{x^2}\,dx$ equalsThe value of $\displaystyle\int_0^{\pi/2} \log\!\left(\dfrac{4+3 in x}{4+3\cos x}\right)dx