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}

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}