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Popular >

integral of x(x^2-8)

Solution

\int x (x^{2} - 8) d x

Solution

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

Solution steps

\int x (x^{2} - 8) d x

Expand

x (x^{2} - 8) : x^{3} - 8 x

= \int x^{3} - 8 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 8 x d x

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

\int 8 x d x = 4 x^{2}

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

Add a constant to the solution

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

Popular Examples

integral of 2-3x^2

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

integral of x^2-50x+700

\int x^{2} - 50 x + 700 d x

integral of 2/2

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

integral of e^{x^4+1}

\int e^{x^{4} + 1} d x

integral of (3sqrt(ln(x)))/x

\int \frac{3 ln ( x )}{x} d x

Frequently Asked Questions (FAQ)

What is the integral of x(x^2-8) ?
The integral of x(x^2-8) is (x^4)/4-4x^2+C