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

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

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

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

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

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

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

then

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

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

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

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

\frac{5 s}{s ^{2} + 4 s + 5}

(2 y + 2 t - 9) d t + (4 y + 2 t - 1) d y = 0

\int (3 - x)^{2} d x

f^{'} (x) = f (x) (1 - f (x))

\frac{d}{d t} (2 t^{3})

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