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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (e^{- x} - e^{- 2 x})

x \to 0 lim ([x])

\int \frac{1}{x x ^{4} - 36} d x

x^{2} - x y - y^{2} = 1, (2, 1)

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

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