Integral of $$$y^{x}$$$ with respect to $$$x$$$

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

Find $$$\int y^{x}\, dx$$$.

Apply the exponential rule $$$\int{a^{x} d x} = \frac{a^{x}}{\ln{\left(a \right)}}$$$ with $$$a=y$$$:

$${\color{red}{\int{y^{x} d x}}} = {\color{red}{\frac{y^{x}}{\ln{\left(y \right)}}}}$$

Therefore,

$$\int{y^{x} d x} = \frac{y^{x}}{\ln{\left(y \right)}}$$

Add the constant of integration:

$$\int{y^{x} d x} = \frac{y^{x}}{\ln{\left(y \right)}}+C$$

$$$\int y^{x}\, dx = \frac{y^{x}}{\ln\left(y\right)} + C$$$A

Please try a new game Rotatly