What is the integral of (50+y)/(5x+1) ?

The integral of (50+y)/(5x+1) is 1/(1+5x)(50y+(y^2)/2)+C

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integral of (50+y)/(5x+1)

\int \frac{50 + y}{5 x + 1}

\frac{1}{1 + 5 x} (50 y + \frac{y ^{2}}{2}) + C

Solution steps

\int \frac{50 + y}{5 x + 1} d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{1 + 5 x} \cdot \int 50 + y d y

Apply the Sum Rule:

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

= \frac{1}{1 + 5 x} (\int 50 d y + \int y d y)

\int 50 d y = 50 y

\int y d y = \frac{y ^{2}}{2}

= \frac{1}{1 + 5 x} (50 y + \frac{y ^{2}}{2})

Add a constant to the solution

= \frac{1}{1 + 5 x} (50 y + \frac{y ^{2}}{2}) + C

What is the integral of (50+y)/(5x+1) ?
The integral of (50+y)/(5x+1) is 1/(1+5x)(50y+(y^2)/2)+C