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