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}

y = 4 sin (5 x - 2)

(t^{2} + 1) \frac{d y}{d t} = y t - y

n = 1 \sum \infty \frac{1}{n 8 ^{n}}

\int \frac{1}{3 + 25 x ^{2}} d x

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

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}