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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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