What is the integral of x^5+2x^3+x ?

The integral of x^5+2x^3+x is (x^6)/6+(x^4)/2+(x^2)/2+C

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integral of x^5+2x^3+x

\int x^{5} + 2 x^{3} + x d x

\frac{x ^{6}}{6} + \frac{x ^{4}}{2} + \frac{x ^{2}}{2} + C

Solution steps

\int x^{5} + 2 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^{5} d x + \int 2 x^{3} d x + \int x d x

\int x^{5} d x = \frac{x ^{6}}{6}

\int 2 x^{3} d x = \frac{x ^{4}}{2}

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

= \frac{x ^{6}}{6} + \frac{x ^{4}}{2} + \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{6}}{6} + \frac{x ^{4}}{2} + \frac{x ^{2}}{2} + C

\frac{d}{d x} (x + 60)

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

What is the integral of x^5+2x^3+x ?
The integral of x^5+2x^3+x is (x^6)/6+(x^4)/2+(x^2)/2+C