Solve 1 / 1 ^ 2 wrt y = ∫ 1 / 1 - x ^2dx

$$\frac { 1 } { 1 ^ { 2 } } d y = \int \frac { 1 } { 1 - x ^ { 2 } } d x$$

Solve for d

$$\left\{\begin{matrix}d=\frac{С}{y}-\frac{\ln(\frac{|x-1|}{|x+1|})}{2y}\text{, }&y\neq 0\text{ and }|x|\neq 1\\d\in \mathrm{R}\text{, }&\left(x=-\frac{1-e^{2С}}{e^{2С_{1}}+1}\text{ and }y=0\right)\text{ or }\left(x=-\frac{e^{2С_{2}}+1}{1-e^{2С_{3}}}\text{ and }С_{4}\neq 0\text{ and }y=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Rewrite 1^{2} as 1\times 1. Cancel out 1 in both numerator and denominator.

$$\frac{1}{1}dy=\int \frac{1}{1-x^{2}}\mathrm{d}x$$

Anything divided by one gives itself.

$$1dy=\int \frac{1}{1-x^{2}}\mathrm{d}x$$

Reorder the terms.

$$dy=\int \frac{1}{-x^{2}+1}\mathrm{d}x$$

The equation is in standard form.

$$yd=-\frac{\ln(\frac{|x-1|}{|x+1|})}{2}+С$$

Divide both sides by y.

$$\frac{yd}{y}=\frac{-\frac{\ln(\frac{|x-1|}{|x+1|})}{2}+С}{y}$$

Dividing by y undoes the multiplication by y.

$$d=\frac{-\frac{\ln(\frac{|x-1|}{|x+1|})}{2}+С}{y}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{С}{d}-\frac{\ln(\frac{|x-1|}{|x+1|})}{2d}\text{, }&d\neq 0\text{ and }|x|\neq 1\\y\in \mathrm{R}\text{, }&\left(x=-\frac{1-e^{2С}}{e^{2С_{1}}+1}\text{ and }d=0\right)\text{ or }\left(x=-\frac{e^{2С_{2}}+1}{1-e^{2С_{3}}}\text{ and }С_{4}\neq 0\text{ and }d=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Rewrite 1^{2} as 1\times 1. Cancel out 1 in both numerator and denominator.

$$\frac{1}{1}dy=\int \frac{1}{1-x^{2}}\mathrm{d}x$$

Anything divided by one gives itself.

$$1dy=\int \frac{1}{1-x^{2}}\mathrm{d}x$$

Reorder the terms.

$$dy=\int \frac{1}{-x^{2}+1}\mathrm{d}x$$

The equation is in standard form.

$$dy=-\frac{\ln(\frac{|x-1|}{|x+1|})}{2}+С$$

Divide both sides by d.

$$\frac{dy}{d}=\frac{-\frac{\ln(\frac{|x-1|}{|x+1|})}{2}+С}{d}$$

Dividing by d undoes the multiplication by d.

$$y=\frac{-\frac{\ln(\frac{|x-1|}{|x+1|})}{2}+С}{d}$$