What is the integral of (2y)/x ?

The integral of (2y)/x is 2yln|x|+C

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integral of (2y)/x

\int \frac{2 y}{x} d x

2 y ln ∣ x ∣ + C

Solution steps

\int \frac{2 y}{x} d x

Take the constant out:

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

= 2 y \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 2 y ln ∣ x ∣

Add a constant to the solution

= 2 y ln ∣ x ∣ + C

\frac{\partial}{\partial r} (\frac{1}{3} π r^{2} h)

f (x) = \frac{( 5 x - 2 )}{( x ^{2} + 1 )}

\int_{0}^{\frac{π}{8}} sec^{2} (2 x) d x

\int_{0}^{\frac{π}{6}} 1

x \to 0 - lim (x^{s i n (x)})