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

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

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

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

ln x^{2} + x + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x^{2} + x

= ln x^{2} + x

Add a constant to the solution

= ln x^{2} + x + C

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