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

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

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integral of-1/(2x+2)

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

- \frac{1}{2} ln ∣ 2 x + 2 ∣ + C

Solution steps

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

Take the constant out:

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

= - \int \frac{1}{2 x + 2} 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 + 2

= - \frac{1}{2} ln ∣ 2 x + 2 ∣

Add a constant to the solution

= - \frac{1}{2} ln ∣ 2 x + 2 ∣ + C

x \to 2 - lim (\frac{6}{x - 2})

f (x) = 6 x^{4}

\int_{- 1}^{2} 5 x + 6 d x

n = 1 \sum \infty (- 2)^{n} (x)^{n}

y^{^{''}} + 8 y^{^{'}} - 20 y = 0