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

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

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integral of ln(x^2+x)

\int ln (x^{2} + x) d x

x ln (x^{2} + x) - 2 x + ln ∣ x + 1 ∣ + C

Solution steps

\int ln (x^{2} + x) d x

Apply Integration By Parts

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

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

\int \frac{2 x + 1}{x + 1} d x = 2 x - ln ∣ x + 1 ∣

= x ln (x^{2} + x) - (2 x - ln ∣ x + 1 ∣)

Simplify

= x ln (x^{2} + x) - 2 x + ln ∣ x + 1 ∣

Add a constant to the solution

= x ln (x^{2} + x) - 2 x + ln ∣ x + 1 ∣ + C

\frac{\partial}{\partial x} (z arctan (y x))

\int \frac{1}{4 e ^{- 3 x} + e ^{3 x}} d x

\int_{- 2}^{1} (x - 6 ∣ x ∣) d x

x \to 0 lim (- x^{4})

y^{^{''}} + 4 y = x - \frac{x ^{2}}{20}

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