What is the integral of (x/y) ?

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

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integral of (x/y)

\int (\frac{x}{y}) d y

x ln ∣ y ∣ + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{y} d y = ln (∣ y ∣)

= x ln ∣ y ∣

Add a constant to the solution

= x ln ∣ y ∣ + C

\int_{4}^{\infty} e^{4 x} d x

\int 5 - x^{2} d x

\int x^{3} \cdot 1 - x^{2} d x

y = x^{2} (x - 11), [- 1, 12]

n = 1 \sum \infty \frac{1}{2 n + 7}