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

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

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

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

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

Solution steps

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

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

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

\int 5 d x = 5 x

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

Add a constant to the solution

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

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