Solve ∫ xe^x^2 wrt y

$$\int x e ^ { x ^ { 2 } } d y$$

Evaluate

$$xye^{x^{2}}+С$$

Solution Steps

Find the integral of xe^{x^{2}} using the table of common integrals rule \int a\mathrm{d}y=ay.

$$xe^{x^{2}}y$$

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

$$xe^{x^{2}}y+С$$

Differentiate w.r.t. x

$$y\left(2x^{2}+1\right)e^{x^{2}}$$