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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = x^{2} + x + 1

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

Add a constant to the solution

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

(x + x) y^{^{'}} = y + y

n = 1 \sum \infty 2 \cdot 0. 2^{n}

3 x^{2} e^{y} + (x^{3} e^{y} - 1) y^{^{'}} = 0

\int_{1}^{8} \frac{3}{x} d x

\int \frac{( x ^{2} )}{( 15 + 6 x - 9 x ^{2} ) ^{\frac{3}{2}}} d x

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