What is the integral of (3x^2)/(x^2+2x+1) ?

The integral of (3x^2)/(x^2+2x+1) is 3(-(x^2)/(x+1)+2(x+1-ln|x+1|))+C

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integral of (3x^2)/(x^2+2x+1)

\int \frac{3 x ^{2}}{x ^{2} + 2 x + 1} d x

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

Solution steps

\int \frac{3 x ^{2}}{x ^{2} + 2 x + 1} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \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

= 3 (- \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 ∣)

= 3 (- \frac{x ^{2}}{x + 1} - (- 2 (x + 1 - ln ∣ x + 1 ∣)))

Simplify

= 3 (- \frac{x ^{2}}{x + 1} + 2 (x + 1 - ln ∣ x + 1 ∣))

Add a constant to the solution

= 3 (- \frac{x ^{2}}{x + 1} + 2 (x + 1 - ln ∣ x + 1 ∣)) + C

x \to 0 lim (\frac{x ^{2}}{x})

\frac{d}{d x} (\frac{1}{x + x})

\frac{125}{x ^{2} + 49}

\int x^{2} 4 x + 6 d x

\int 3 z^{2} sin (x) - 4 d z

What is the integral of (3x^2)/(x^2+2x+1) ?
The integral of (3x^2)/(x^2+2x+1) is 3(-(x^2)/(x+1)+2(x+1-ln|x+1|))+C