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Integral of $$$x^{33}$$$
Related calculator: Definite and Improper Integral Calculator
Your Input
Find $$$\int x^{33}\, dx$$$.
Solution
Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=33$$$:
$${\color{red}{\int{x^{33} d x}}}={\color{red}{\frac{x^{1 + 33}}{1 + 33}}}={\color{red}{\left(\frac{x^{34}}{34}\right)}}$$
Therefore,
$$\int{x^{33} d x} = \frac{x^{34}}{34}$$
Add the constant of integration:
$$\int{x^{33} d x} = \frac{x^{34}}{34}+C$$
Answer
$$$\int x^{33}\, dx = \frac{x^{34}}{34} + C$$$A
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