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

Apply the Power Rule

= - \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

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

\frac{d}{d x} (e^{x^{\frac{1}{2}}})

t an g e n t f (x) = 2 x^{3} - 3 x^{2} + 3, at x = 1

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

\frac{d}{d x} (x^{- l n (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