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Integral of $$$i^{10}$$$
Related calculator: Definite and Improper Integral Calculator
Your Input
Find $$$\int i^{10}\, di$$$.
Solution
Apply the power rule $$$\int i^{n}\, di = \frac{i^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=10$$$:
$${\color{red}{\int{i^{10} d i}}}={\color{red}{\frac{i^{1 + 10}}{1 + 10}}}={\color{red}{\left(\frac{i^{11}}{11}\right)}}$$
Therefore,
$$\int{i^{10} d i} = \frac{i^{11}}{11}$$
Add the constant of integration:
$$\int{i^{10} d i} = \frac{i^{11}}{11}+C$$
Answer
$$$\int i^{10}\, di = \frac{i^{11}}{11} + C$$$A
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