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

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

Popular >

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

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

- \frac{1}{2} ln ∣ x + 1 ∣ + C

Solution steps

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

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}{x + 1} d x

Simplify

= (- \frac{1}{2}) \cdot \int \frac{1}{x + 1} d x

Apply u-substitution

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

= (- \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 = x + 1

= (- \frac{1}{2}) ln ∣ x + 1 ∣

Simplify

= - \frac{1}{2} ln ∣ x + 1 ∣

Add a constant to the solution

= - \frac{1}{2} ln ∣ x + 1 ∣ + C

\int x^{4} ln (3 x) d x

(x^{2} + 1)^{3} (x^{2} + 2)^{6}

\int_{- l n (4)}^{0} 33 e^{t} d t

\frac{1}{6 x ^{2} + 5}

\int 15 x^{29} cos (x^{15}) d x

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