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

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

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integral of (3x^4-2x^3+5)

\int (3 x^{4} - 2 x^{3} + 5) d x

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

Solution steps

\int 3 x^{4} - 2 x^{3} + 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 3 x^{4} d x - \int 2 x^{3} d x + \int 5 d x

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

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

\int 5 d x = 5 x

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

Add a constant to the solution

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

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