What is the integral of (8y)/x ?

The integral of (8y)/x is 8yln|x|+C

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integral of (8y)/x

\int \frac{8 y}{x} d x

8 y ln ∣ x ∣ + C

Solution steps

\int \frac{8 y}{x} d x

Take the constant out:

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

= 8 y \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 8 y ln ∣ x ∣

Add a constant to the solution

= 8 y ln ∣ x ∣ + C

x \to \infty lim (\frac{3.4}{0.1 + 33.9 e ^{- 0.5678 x}})

t^{3} 1 (t)

\frac{d}{d x} (\frac{ln ( x )}{5 ln ( x ) + 4})

\int_{1}^{4} t ln (t) d t

y = x + 3 y = x + 1 y = - x + 1