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

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

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integral of 3x^3-2x+1

\int 3 x^{3} - 2 x + 1 d x

\frac{3 x ^{4}}{4} - x^{2} + x + C

Solution steps

\int 3 x^{3} - 2 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 3 x^{3} d x - \int 2 x d x + \int 1 d x

\int 3 x^{3} d x = \frac{3 x ^{4}}{4}

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

\int 1 d x = x

= \frac{3 x ^{4}}{4} - x^{2} + x

Add a constant to the solution

= \frac{3 x ^{4}}{4} - x^{2} + x + C

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