What is the integral of 1/(2t) ?

The integral of 1/(2t) is 1/2 ln|t|+C

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integral of 1/(2t)

\int \frac{1}{2 t} d t

\frac{1}{2} ln ∣ t ∣ + C

Solution steps

\int \frac{1}{2 t} d t

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{t} d t

Use the common integral:

\int \frac{1}{t} d t = ln (∣ t ∣)

= \frac{1}{2} ln ∣ t ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ t ∣ + C

f (x) = x^{3}, at x = 2

\int 4 x arctan (x) d x

x \to 9 lim (\frac{1}{x - 9})

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

\frac{1}{y} \frac{d y}{d x} = e^{x} + ln (y)