What is the integral of (5/x) ?

The integral of (5/x) is 5ln|x|+C

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integral of (5/x)

\int (\frac{5}{x}) d x

5 ln ∣ x ∣ + C

Solution steps

\int \frac{5}{x} d x

Take the constant out:

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

= 5 \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 5 ln ∣ x ∣

Add a constant to the solution

= 5 ln ∣ x ∣ + C

sin (7 x) + cos (2 x)

\int 8 sin^{3} (t) cos (t) d t

y = cos^{2} (t)

\int \frac{3 x}{x ^{2} + 2} d x

f (x) = (3 x^{3})^{0.5}