What is the integral of Q^2-4Q+10 ?

The integral of Q^2-4Q+10 is (Q^3)/3-2Q^2+10Q+C

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integral of Q^2-4Q+10

\int Q^{2} - 4 Q + 10 d Q

\frac{Q ^{3}}{3} - 2 Q^{2} + 10 Q + C

Solution steps

\int Q^{2} - 4 Q + 10 d Q

Apply the Sum Rule:

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

= \int Q^{2} d Q - \int 4 Q d Q + \int 10 d Q

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

\int 4 Q d Q = 2 Q^{2}

\int 10 d Q = 10 Q

= \frac{Q ^{3}}{3} - 2 Q^{2} + 10 Q

Add a constant to the solution

= \frac{Q ^{3}}{3} - 2 Q^{2} + 10 Q + C

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What is the integral of Q^2-4Q+10 ?
The integral of Q^2-4Q+10 is (Q^3)/3-2Q^2+10Q+C