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

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

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integral of (5x^3+2x^2-6x+3)

\int (5 x^{3} + 2 x^{2} - 6 x + 3) d x

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

Solution steps

\int 5 x^{3} + 2 x^{2} - 6 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 5 x^{3} d x + \int 2 x^{2} d x - \int 6 x d x + \int 3 d x

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

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

\int \frac{1}{x \cdot ln ( x )} d x

\frac{d y}{d t} - 2 t y = 1

x \to 3 - lim (2 x + 1)

y = 6 x^{4} - 6 x^{2}, y = 3 x^{2}, x = 0

\frac{d y}{d t} + e^{t} y = 10 e^{t}

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