What is the solution for (dy)/(dx)=x^7-1/(x^7) ?

The solution for (dy)/(dx)=x^7-1/(x^7) is y=(x^8)/8+1/(6x^6)+c_{1}

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(dy)/(dx)=x^7-1/(x^7)

\frac{d y}{d x} = x^{7} - \frac{1}{x ^{7}}

y = \frac{x ^{8}}{8} + \frac{1}{6 x ^{6}} + c_{1}

Solution steps

\frac{d y}{d x} = x^{7} - \frac{1}{x ^{7}}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = x^{7} - \frac{1}{x ^{7}}

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

then

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

y = \int x^{7} - \frac{1}{x ^{7}} d x

\int x^{7} - \frac{1}{x ^{7}} d x = \frac{x ^{8}}{8} + \frac{1}{6 x ^{6}} + c_{1}

y = \frac{x ^{8}}{8} + \frac{1}{6 x ^{6}} + c_{1}

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What is the solution for (dy)/(dx)=x^7-1/(x^7) ?
The solution for (dy)/(dx)=x^7-1/(x^7) is y=(x^8)/8+1/(6x^6)+c_{1}