Integral of $$$b^{c}$$$ with respect to $$$b$$$

The calculator will find the integral/antiderivative of $$$b^{c}$$$ with respect to $$$b$$$, with steps shown.

Find $$$\int b^{c}\, db$$$.

Apply the power rule $$$\int b^{n}\, db = \frac{b^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=c$$$:

$${\color{red}{\int{b^{c} d b}}}={\color{red}{\frac{b^{c + 1}}{c + 1}}}={\color{red}{\frac{b^{c + 1}}{c + 1}}}$$

Therefore,

$$\int{b^{c} d b} = \frac{b^{c + 1}}{c + 1}$$

Add the constant of integration:

$$\int{b^{c} d b} = \frac{b^{c + 1}}{c + 1}+C$$

$$$\int b^{c}\, db = \frac{b^{c + 1}}{c + 1} + C$$$A