What is the solution for f^'(x)=((5x+1))/(5x) ?

The solution for f^'(x)=((5x+1))/(5x) is f(x)=x+1/5 ln(x)+c_{1}

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f^'(x)=((5x+1))/(5x)

f^{^{'}} (x) = \frac{( 5 x + 1 )}{5 x}

f (x) = x + \frac{1}{5} ln (x) + c_{1}

Solution steps

f^{'} (x) = \frac{( 5 x + 1 )}{5 x}

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

then

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

f (x) = \int \frac{5 x + 1}{5 x} d x

\int \frac{5 x + 1}{5 x} d x = x + \frac{1}{5} ln (x) + c_{1}

f (x) = x + \frac{1}{5} ln (x) + c_{1}

\frac{\partial}{\partial x} (m sin (2 m x + 2 n y))

\int_{0}^{1} 2 x - x^{2} d x

\frac{\partial}{\partial x} (5 sin (x y))

\frac{d}{d x} (\frac{x ^{2}}{3 + x})

y^{^{'}} + 6 x y^{2} = 0

What is the solution for f^'(x)=((5x+1))/(5x) ?
The solution for f^'(x)=((5x+1))/(5x) is f(x)=x+1/5 ln(x)+c_{1}