What is the integral of 1/(x+!) ?

The integral of 1/(x+!) is 1/(+!)ln|x|+C

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integral of 1/(x+!)

\int \frac{1}{x + !} d x

\frac{1}{+ !} ln ∣ x ∣ + C

Solution steps

\int \frac{1}{x + !} d x

Take the constant out:

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

= \frac{1}{+ !} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{+ !} ln ∣ x ∣

Add a constant to the solution

= \frac{1}{+ !} ln ∣ x ∣ + C

\frac{d}{d x} ((2 x - 1) (3 x + 4) (x + 7))

\frac{d}{d x} (\frac{y ^{2} - 3 x ^{2}}{y ^{4}})

\frac{\partial}{\partial x} (+ 6 - 5 + 6 x)

n = 0 \sum \infty \frac{2}{7 ^{n}}

x \to 2 - lim (arcsin (x - 1))