Solve ∫ {(e)^frac{1+y{1-y wrt y

$$\int{ {(e)^{ \frac{ 1+y }{ 1-y } }} }d y$$

Evaluate

$$xe^{\frac{y+1}{-y+1}}+С$$

Solution Steps

Find the integral of e^{\frac{1+y}{1-y}} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$e^{\frac{1+y}{1-y}}x$$

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.

$$e^{\frac{1+y}{1-y}}x+С$$

Differentiate w.r.t. x

$$e^{\frac{y+1}{1-y}}$$