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Integral of $$$x^{12}$$$
Related calculator: Definite and Improper Integral Calculator
Your Input
Find $$$\int x^{12}\, dx$$$.
Solution
Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=12$$$:
$${\color{red}{\int{x^{12} d x}}}={\color{red}{\frac{x^{1 + 12}}{1 + 12}}}={\color{red}{\left(\frac{x^{13}}{13}\right)}}$$
Therefore,
$$\int{x^{12} d x} = \frac{x^{13}}{13}$$
Add the constant of integration:
$$\int{x^{12} d x} = \frac{x^{13}}{13}+C$$
Answer
$$$\int x^{12}\, dx = \frac{x^{13}}{13} + C$$$A
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