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Popular >

integral of x(x^2-3)

Solution

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

Solution

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

Solution steps

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

Expand

x (x^{2} - 3) : x^{3} - 3 x

= \int x^{3} - 3 x 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 x^{3} d x - \int 3 x d x

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

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

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

Add a constant to the solution

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

Popular Examples

derivative of-25(x/(x^2+1))

\frac{d}{d x} (- 25 (\frac{x}{x ^{2} + 1}))

integral of (8x+9)

\int (8 x + 9) d x

integral of cos(9x)

\int cos (9 x) d x

integral of cot(1/8 x)

\int cot (\frac{1}{8} x) d x

derivative of (4x^{3/2}-x^3+8/x)

\frac{d}{d x} (\frac{4 x ^{\frac{3}{2}} - x ^{3} + 8}{x})

Frequently Asked Questions (FAQ)

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