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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

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

Substitute back

u = 1 + x + x^{2}

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

Add a constant to the solution

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

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