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Popular >

integral of x^3+x

Solution

\int x^{3} + x d x

Solution

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

Solution steps

\int x^{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 x d x

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

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

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

Add a constant to the solution

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

Graph

Popular Examples

(dy)/(dx)=6x^2e^{-y}

\frac{d y}{d x} = 6 x^{2} e^{- y}

integral of (y^3+1.8y^2-2.4y)

\int (y^{3} + 1.8 y^{2} - 2.4 y) d y

limit as x approaches-2 of (3x-1)/x

x \to - 2 lim (\frac{3 x - 1}{x})

(\partial)/(\partial x)((4x)/(sqrt(x^2+2)))

\frac{\partial}{\partial x} (\frac{4 x}{x ^{2} + 2})

slope of (0,4),(1,1)slope

(0, 4), (1, 1)

Frequently Asked Questions (FAQ)

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