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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = x^{2} + x + 1

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

Add a constant to the solution

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

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