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

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

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

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

\frac{1}{2} ln x^{2} + 2 x + C

Solution steps

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

= \frac{1}{2} ln x^{2} + 2 x

Add a constant to the solution

= \frac{1}{2} ln x^{2} + 2 x + C

n = 1 \sum \infty \frac{1}{3} (\frac{e}{2})^{n}

\int \frac{x ^{5} + 2 x ^{3} - 3 x}{( x ^{2} + 1 ) ^{3}} d x

\int 2 e^{y^{2}} d y

e^{2 x^{x}}

\int_{1}^{4} (x + x) d x

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