What is the integral of (3x^4-5x^3-x-6) ?

The integral of (3x^4-5x^3-x-6) is (3x^5)/5-(5x^4)/4-(x^2)/2-6x+C

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integral of (3x^4-5x^3-x-6)

\int (3 x^{4} - 5 x^{3} - x - 6) d x

\frac{3 x ^{5}}{5} - \frac{5 x ^{4}}{4} - \frac{x ^{2}}{2} - 6 x + C

Solution steps

\int 3 x^{4} - 5 x^{3} - x - 6 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 5 x^{3} d x - \int x d x - \int 6 d x

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

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

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

\int 6 d x = 6 x

= \frac{3 x ^{5}}{5} - \frac{5 x ^{4}}{4} - \frac{x ^{2}}{2} - 6 x

Add a constant to the solution

= \frac{3 x ^{5}}{5} - \frac{5 x ^{4}}{4} - \frac{x ^{2}}{2} - 6 x + C

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What is the integral of (3x^4-5x^3-x-6) ?
The integral of (3x^4-5x^3-x-6) is (3x^5)/5-(5x^4)/4-(x^2)/2-6x+C