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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

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