What is the integral of-3/(2x) ?

The integral of-3/(2x) is -3/2 ln|x|+C

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integral of-3/(2x)

\int - \frac{3}{2 x} d x

- \frac{3}{2} ln ∣ x ∣ + C

Solution steps

\int - \frac{3}{2 x} d x

Take the constant out:

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

= - \frac{3}{2} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= - \frac{3}{2} ln ∣ x ∣

Add a constant to the solution

= - \frac{3}{2} ln ∣ x ∣ + C

\int e^{a r c s i n (x)} d x

cos (π x)

\frac{1 - sec ( x )}{tan ( x )}

\int \frac{1}{a ^{2} x ^{2} + 8 a x + 15} d x

\int \frac{x - 2}{x + 2} d x