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

The integral of (2x+1)(x^2+x+1)^3 is ((x^2+x+1)^4)/4+C

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

\int (2 x + 1) (x^{2} + x + 1)^{3} d x

\frac{( x ^{2} + x + 1 ) ^{4}}{4} + C

Solution steps

\int (2 x + 1) (x^{2} + x + 1)^{3} d x

Apply u-substitution

= \int u^{3} d u

Apply the Power Rule

= \frac{u ^{4}}{4}

Substitute back

u = x^{2} + x + 1

= \frac{( x ^{2} + x + 1 ) ^{4}}{4}

Add a constant to the solution

= \frac{( x ^{2} + x + 1 ) ^{4}}{4} + C

What is the integral of (2x+1)(x^2+x+1)^3 ?
The integral of (2x+1)(x^2+x+1)^3 is ((x^2+x+1)^4)/4+C