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

\frac{\partial}{\partial x} (ln (1 + x^{2} + y))

\int t^{3} e^{- t} d t

f (x) = (x + 2)^{2} e^{- x}

x \to - 1 lim (\frac{2 - 2}{x + 1})