What is the integral of 1/((2x+5)) ?

The integral of 1/((2x+5)) is 1/2 ln|2x+5|+C

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integral of 1/((2x+5))

\int \frac{1}{( 2 x + 5 )} d x

\frac{1}{2} ln ∣ 2 x + 5 ∣ + C

Solution steps

\int \frac{1}{2 x + 5} d x

Apply u-substitution

: \int \frac{1}{2 u} d u

= \int \frac{1}{2 u} d u

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}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = 2 x + 5

= \frac{1}{2} ln ∣ 2 x + 5 ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ 2 x + 5 ∣ + C

\frac{d}{d x} (\frac{1}{x ^{2}})

\int \frac{2}{1 + x ^{4}} d x

\frac{1}{6 x}

\int e^{t y} (4 y + 1) d y

\int e^{2 x} \cdot sin (x) d x

What is the integral of 1/((2x+5)) ?
The integral of 1/((2x+5)) is 1/2 ln|2x+5|+C