What is the integral of 2x^3+5x^2-3x+1 ?

The integral of 2x^3+5x^2-3x+1 is (x^4)/2+(5x^3)/3-(3x^2)/2+x+C

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integral of 2x^3+5x^2-3x+1

\int 2 x^{3} + 5 x^{2} - 3 x + 1 d x

\frac{x ^{4}}{2} + \frac{5 x ^{3}}{3} - \frac{3 x ^{2}}{2} + x + C

Solution steps

\int 2 x^{3} + 5 x^{2} - 3 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 2 x^{3} d x + \int 5 x^{2} d x - \int 3 x d x + \int 1 d x

\int 2 x^{3} d x = \frac{x ^{4}}{2}

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

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

\int 1 d x = x

= \frac{x ^{4}}{2} + \frac{5 x ^{3}}{3} - \frac{3 x ^{2}}{2} + x

Add a constant to the solution

= \frac{x ^{4}}{2} + \frac{5 x ^{3}}{3} - \frac{3 x ^{2}}{2} + x + C

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What is the integral of 2x^3+5x^2-3x+1 ?
The integral of 2x^3+5x^2-3x+1 is (x^4)/2+(5x^3)/3-(3x^2)/2+x+C