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

The solution for dy=(x+6)/(x+1)dx is y=5ln(x+1)+x+c_{1}

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dy=(x+6)/(x+1)dx

d y = \frac{x + 6}{x + 1} d x

y = 5 ln (x + 1) + x + c_{1}

Solution steps

d y = \frac{x + 6}{x + 1} d x

Let

y

be the dependent variable. Divide by

d x

\frac{d y}{d x} = \frac{x + 6}{x + 1}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

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

then

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

y = \int \frac{x + 6}{x + 1} d x

\int \frac{x + 6}{x + 1} d x = 5 ln (x + 1) + x + c_{1}

y = 5 ln (x + 1) + x + c_{1}

d er i v a t i v e y = 4 sin (5 x - 2)

\int cot^{6} (x) d x

s l o p e (- 7.6) (4.2)

\frac{d}{d t} (\frac{t}{t - 1})

d er i v a t i v e 4 t e^{- t}

What is the solution for dy=(x+6)/(x+1)dx ?
The solution for dy=(x+6)/(x+1)dx is y=5ln(x+1)+x+c_{1}