What is the integral of 2x^3+3x^2-4x+5 ?

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

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integral of 2x^3+3x^2-4x+5

\int 2 x^{3} + 3 x^{2} - 4 x + 5 d x

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

Solution steps

\int 2 x^{3} + 3 x^{2} - 4 x + 5 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 3 x^{2} d x - \int 4 x d x + \int 5 d x

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

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

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

\int 5 d x = 5 x

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

Add a constant to the solution

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

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