What is the solution for (dy)/(dx)=((4x)/((1+x^2)^{1/3)}) ?

The solution for (dy)/(dx)=((4x)/((1+x^2)^{1/3)}) is y=3(x^2+1)^{2/3}+c_{1}

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(dy)/(dx)=((4x)/((1+x^2)^{1/3)})

\frac{d y}{d x} = (\frac{4 x}{( 1 + x ^{2} ) ^{\frac{1}{3}}})

y = 3 (x^{2} + 1)^{\frac{2}{3}} + c_{1}

Solution steps

\frac{d y}{d x} = (\frac{4 x}{( 1 + x ^{2} ) ^{\frac{1}{3}}})

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = (\frac{4 x}{( 1 + x ^{2} ) ^{\frac{1}{3}}})

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

then

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

y = \int \frac{4 x}{( 1 + x ^{2} ) ^{\frac{1}{3}}} d x

\int \frac{4 x}{( 1 + x ^{2} ) ^{\frac{1}{3}}} d x = 3 (x^{2} + 1)^{\frac{2}{3}} + c_{1}

y = 3 (x^{2} + 1)^{\frac{2}{3}} + c_{1}

What is the solution for (dy)/(dx)=((4x)/((1+x^2)^{1/3)}) ?
The solution for (dy)/(dx)=((4x)/((1+x^2)^{1/3)}) is y=3(x^2+1)^{2/3}+c_{1}