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

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

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integral of (3x)/(x^2)

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

3 ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

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

= 3 \cdot \int \frac{x}{x ^{2}} d x

Cancel the common factor:

x

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 3 ln ∣ x ∣

Add a constant to the solution

= 3 ln ∣ x ∣ + C

f^{^{'}} (x) = 3 sec (x)

\int_{- 1}^{4} \frac{x}{5 + x} d x

x \to 3 - lim (\frac{∣ x - 3 ∣}{x - 3})

\frac{d}{d x} (arcsin (1 - x))

\frac{d y}{d t} = 100 - y, y (0) = 15