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Popular Calculus >

integral of x(x^2-5)

Solution

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

Solution

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

Solution steps

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

Expand

x (x^{2} - 5) : x^{3} - 5 x

= \int x^{3} - 5 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 5 x d x

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

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

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

Add a constant to the solution

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

Graph

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\int 1 - \frac{4}{x ^{2}} d x

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\int \frac{( sec ^{2} ( \frac{1}{x ^{3}} ) )}{x ^{4}} d x

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\int - 4 cos (x) sin (x) d x

integral of ((7+x+x^2))/(sqrt(x))

\int \frac{( 7 + x + x ^{2} )}{x} d x

Frequently Asked Questions (FAQ)

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