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}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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}

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}