Solve for: integral of x ^ 5 x

Expression: $$\int x ^ { 5 } d x$$

Since $\int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1}$ for $k\neq -1$, replace $\int x^{5}\mathrm{d}x$ with $\frac{x^{6}}{6}$.

$$\frac{x^{6}}{6}$$

If $F\left(x\right)$ is an antiderivative of $f\left(x\right)$, then the set of all antiderivatives of $f\left(x\right)$ is given by $F\left(x\right)+C$. Therefore, add the constant of integration $C\in \mathrm{R}$ to the result.

$$\frac{x^{6}}{6}+С$$