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Popular Calculus >

integral of (2x^3+x)

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

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