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

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

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integral of (1+u+u^2)

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

u + \frac{u ^{2}}{2} + \frac{u ^{3}}{3} + C

Solution steps

\int 1 + u + u^{2} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int 1 d u = u

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

\int u^{2} d u = \frac{u ^{3}}{3}

= u + \frac{u ^{2}}{2} + \frac{u ^{3}}{3}

Add a constant to the solution

= u + \frac{u ^{2}}{2} + \frac{u ^{3}}{3} + C

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