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

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

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integral of ln(x+x^2)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int x^{2} (7 - x^{3})^{\frac{2}{3}} d x

\frac{d}{d x} (tan (x^{2} - 4 x))

x \to - \infty lim (x^{3} - 5 x^{2})

\int x^{2} \cdot x - 5 d x

y = x^{2} (x^{3} - 1)^{5}

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