Solve ∫ int{x*{(e)^y wrt x}dy

$$\int{ \int{ x \times {(e)^{ y }} }d x }d y$$

Evaluate

$$\frac{x^{3}e^{y}}{6}+Сx+С_{1}$$

Solution Steps

Simplify.

$$\frac{e^{y}x^{3}}{6}+Сx$$

If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$\frac{e^{y}x^{3}}{6}+Сx+С$$

Differentiate w.r.t. x

$$\frac{x^{2}e^{y}}{2}+С$$