What is the integral of (x^4+x^2+x) ?

The integral of (x^4+x^2+x) is (x^5)/5+(x^3)/3+(x^2)/2+C

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integral of (x^4+x^2+x)

\int (x^{4} + x^{2} + x) d x

\frac{x ^{5}}{5} + \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + C

Solution steps

\int x^{4} + x^{2} + 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^{2} d x + \int x d x

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

\int x^{2} d x = \frac{x ^{3}}{3}

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

= \frac{x ^{5}}{5} + \frac{x ^{3}}{3} + \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{5}}{5} + \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + C

\frac{\partial}{\partial x} (x^{8})

y = \frac{1}{2 + 3 x}, (2, \frac{1}{8})

\frac{d}{d x} (\frac{4}{x ^{2} + 1})

x \to 0 lim (\frac{1}{2 x} - \frac{1}{e ^{2 x} - 1})

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

What is the integral of (x^4+x^2+x) ?
The integral of (x^4+x^2+x) is (x^5)/5+(x^3)/3+(x^2)/2+C