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

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

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integral of 5x^3+7x-2

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

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

Solution steps

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

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

\int 7 x d x = \frac{7 x ^{2}}{2}

\int 2 d x = 2 x

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

Add a constant to the solution

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

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