What is the solution for (dy)/(dx)= 1/(6x-42) ?

The solution for (dy)/(dx)= 1/(6x-42) is y= 1/6 ln(6x-42)+c_{1}

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(dy)/(dx)= 1/(6x-42)

\frac{d y}{d x} = \frac{1}{6 x - 42}

y = \frac{1}{6} ln (6 x - 42) + c_{1}

Solution steps

\frac{d y}{d x} = \frac{1}{6 x - 42}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{1}{6 x - 42}

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

then

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

y = \int \frac{1}{6 x - 42} d x

\int \frac{1}{6 x - 42} d x = \frac{1}{6} ln (6 x - 42) + c_{1}

y = \frac{1}{6} ln (6 x - 42) + c_{1}

y = \frac{e ^{4 x^{2} + 1}}{8}

2 x + 5 x

h (x) = x^{2}

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

\int_{0}^{1} \frac{1}{x ^{0.5} ln ( x )} d x

What is the solution for (dy)/(dx)= 1/(6x-42) ?
The solution for (dy)/(dx)= 1/(6x-42) is y= 1/6 ln(6x-42)+c_{1}