Solve ∫ {e}^-frac{y2{2 wrt y

$$\int{ { e }^{ - \frac{ y2 }{ 2 } } }d y$$

Evaluate

$$ye^{-\frac{y_{2}}{2}}+С$$

Solution Steps

Find the integral of \frac{1}{e^{\frac{1}{2}y_{2}}} using the table of common integrals rule \int a\mathrm{d}y=ay.

$$\frac{y}{e^{\frac{1}{2}y_{2}}}$$

Simplify.

$$e^{-\frac{y_{2}}{2}}y$$

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.

$$e^{-\frac{y_{2}}{2}}y+С$$

Differentiate w.r.t. y_2

$$-\frac{ye^{-\frac{y_{2}}{2}}}{2}$$