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Popular Calculus >

integral of x(5-x^2)

Solution

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

Solution

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

Solution steps

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

Expand

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

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

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

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral of ((x^2-x))/(sqrt(3-x^2))

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

integral of ((x^3-1))/((x-1))

\int \frac{( x ^{3} - 1 )}{( x - 1 )} d x

integral of sec(x)tan(x)sqrt(3+sec(x))

\int sec (x) tan (x) 3 + sec (x) d x

integral of sqrt(x)(x^2+3x-8)

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

integral of 1/(x^8+x)

\int \frac{1}{x ^{8} + x} d x

Frequently Asked Questions (FAQ)

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