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Popular >

integral of 2x^3+x+3

Solution

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

Solution

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

Solution steps

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

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

Graph

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\int sin^{4} (\frac{1}{2} x) d x

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\int \frac{1}{( 5 + x ) 1 + x} d x

Frequently Asked Questions (FAQ)

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