What is the integral of (2x^3+5x^2-2x+7) ?

The integral of (2x^3+5x^2-2x+7) is (x^4)/2+(5x^3)/3-x^2+7x+C

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integral of (2x^3+5x^2-2x+7)

\int (2 x^{3} + 5 x^{2} - 2 x + 7) d x

\frac{x ^{4}}{2} + \frac{5 x ^{3}}{3} - x^{2} + 7 x + C

Solution steps

\int 2 x^{3} + 5 x^{2} - 2 x + 7 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 2 x d x + \int 7 d x

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

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

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

\int 7 d x = 7 x

= \frac{x ^{4}}{2} + \frac{5 x ^{3}}{3} - x^{2} + 7 x

Add a constant to the solution

= \frac{x ^{4}}{2} + \frac{5 x ^{3}}{3} - x^{2} + 7 x + C

What is the integral of (2x^3+5x^2-2x+7) ?
The integral of (2x^3+5x^2-2x+7) is (x^4)/2+(5x^3)/3-x^2+7x+C