What is the solution for f^'(x)=xsqrt(7-x^2) ?

The solution for f^'(x)=xsqrt(7-x^2) is f(x)=-1/3 (7-x^2)^{3/2}+c_{1}

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f^'(x)=xsqrt(7-x^2)

f^{^{'}} (x) = x 7 - x^{2}

f (x) = - \frac{1}{3} (7 - x^{2})^{\frac{3}{2}} + c_{1}

Solution steps

f^{'} (x) = x 7 - x^{2}

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

then

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

f (x) = \int x 7 - x^{2} d x

\int x 7 - x^{2} d x = - \frac{1}{3} (7 - x^{2})^{\frac{3}{2}} + c_{1}

f (x) = - \frac{1}{3} (7 - x^{2})^{\frac{3}{2}} + c_{1}

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What is the solution for f^'(x)=xsqrt(7-x^2) ?
The solution for f^'(x)=xsqrt(7-x^2) is f(x)=-1/3 (7-x^2)^{3/2}+c_{1}