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

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

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

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

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

Solution steps

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

\int 3 x^{5} d x = \frac{x ^{6}}{2}

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 6 d x = 6 x

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

Add a constant to the solution

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

\frac{s + 1}{s ^{2} ( s ^{2} + 1 )}

x \to 1 lim (\frac{∣ x - 1 ∣}{x - 1})

\frac{d y}{d x} = 136 x - x y

\frac{d y}{d x} = \frac{2 x}{1 + 2 y}

x^{^{''}} - 3 x^{^{'}} - 10 x = 20 t

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