What is the integral of u/x ?

The integral of u/x is uln|x|+C

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integral of u/x

\int \frac{u}{x} d x

u ln ∣ x ∣ + C

Solution steps

\int \frac{u}{x} d x

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= u ln ∣ x ∣

Add a constant to the solution

= u ln ∣ x ∣ + C

y = sec^{2} (3 x)

\frac{d}{d y} (2 y - \frac{1}{x} + cos (3 x))

\int (x \cdot cos (5 x)) d x

e^{\frac{1}{x}} 0