What is the solution for (dy)/(dx)=(2x)/((1+x^2)) ?

The solution for (dy)/(dx)=(2x)/((1+x^2)) is y=ln(1+x^2)+c_{1}

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(dy)/(dx)=(2x)/((1+x^2))

\frac{d y}{d x} = \frac{2 x}{( 1 + x ^{2} )}

y = ln (1 + x^{2}) + c_{1}

Solution steps

\frac{d y}{d x} = \frac{2 x}{( 1 + x ^{2} )}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{2 x}{( 1 + x ^{2} )}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

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

\int \frac{2 x}{1 + x ^{2}} d x = ln (1 + x^{2}) + c_{1}

y = ln (1 + x^{2}) + c_{1}

What is the solution for (dy)/(dx)=(2x)/((1+x^2)) ?
The solution for (dy)/(dx)=(2x)/((1+x^2)) is y=ln(1+x^2)+c_{1}