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

The solution for f^'(x)=sqrt(5x+1) is f(x)= 2/15 (5x+1)^{3/2}+c_{1}

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

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

f (x) = \frac{2}{15} (5 x + 1)^{\frac{3}{2}} + c_{1}

Solution steps

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

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

then

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

f (x) = \int 5 x + 1 d x

\int 5 x + 1 d x = \frac{2}{15} (5 x + 1)^{\frac{3}{2}} + c_{1}

f (x) = \frac{2}{15} (5 x + 1)^{\frac{3}{2}} + c_{1}

(tan (y))^{^{'}}

x^{^{'}} = - 3 \cdot \frac{x}{300}

\int_{- 2}^{8} 6 x^{2} + 9 d x

\int \frac{4 x}{2 x ^{2} - 6} d x

x \cdot \frac{d y}{d x} + y = \frac{2 y}{1 - y ^{2}}

What is the solution for f^'(x)=sqrt(5x+1) ?
The solution for f^'(x)=sqrt(5x+1) is f(x)= 2/15 (5x+1)^{3/2}+c_{1}