What is the integral of (x^2+5x+1) ?

The integral of (x^2+5x+1) is (x^3)/3+(5x^2)/2+x+C

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integral of (x^2+5x+1)

\int (x^{2} + 5 x + 1) d x

\frac{x ^{3}}{3} + \frac{5 x ^{2}}{2} + x + C

Solution steps

\int x^{2} + 5 x + 1 d x

Apply the Sum Rule:

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

= \int x^{2} d x + \int 5 x d x + \int 1 d x

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 1 d x = x

= \frac{x ^{3}}{3} + \frac{5 x ^{2}}{2} + x

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{5 x ^{2}}{2} + x + C

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What is the integral of (x^2+5x+1) ?
The integral of (x^2+5x+1) is (x^3)/3+(5x^2)/2+x+C