What is the integral of a/x ?

The integral of a/x is aln|x|+C

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integral of a/x

\int \frac{a}{x} d x

a ln ∣ x ∣ + C

Solution steps

\int \frac{a}{x} d x

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= a ln ∣ x ∣

Add a constant to the solution

= a ln ∣ x ∣ + C

(a (t) sin^{3} (t))^{^{'}}

y = sin (7 x)

y^{^{''}} + 4 y^{^{'}} + \frac{17}{4} y = 0

\frac{\partial}{\partial x} (1 - cos (x))

\int cos (\frac{π}{2}) d x