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Popular >

integral of x^4-x

Solution

\int x^{4} - x d x

Solution

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

Solution steps

\int x^{4} - 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^{4} d x - \int x d x

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

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

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

Add a constant to the solution

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

Popular Examples

-y^{''}+y^'+y=0

- y^{^{''}} + y^{^{'}} + y = 0

derivative of (x^2-3x+2/(2x^2+5x-1))

\frac{d}{d x} (\frac{x ^{2} - 3 x + 2}{2 x ^{2} + 5 x - 1})

(\partial)/(\partial y)((2y)/(x+y^2))

\frac{\partial}{\partial y} (\frac{2 y}{x + y ^{2}})

integral of (5sqrt(ln^2(x)+9))/x

\int \frac{5 ln ^{2} ( x ) + 9}{x} d x

(\partial)/(\partial x)(y^2+xy+3y+2x+3)

\frac{\partial}{\partial x} (y^{2} + x y + 3 y + 2 x + 3)

Frequently Asked Questions (FAQ)

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