3.1903 \(\int (\frac{1}{x^5}+x+x^5) \, dx\)

Optimal. Leaf size=22 \[ \frac{x^6}{6}+\frac{x^2}{2}-\frac{1}{4 x^4} \]

[Out]

-1/(4*x^4) + x^2/2 + x^6/6

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Rubi [A]  time = 0.0026291, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{x^6}{6}+\frac{x^2}{2}-\frac{1}{4 x^4} \]

Antiderivative was successfully verified.

[In]

Int[x^(-5) + x + x^5,x]

[Out]

-1/(4*x^4) + x^2/2 + x^6/6

Rubi steps

\begin{align*} \int \left (\frac{1}{x^5}+x+x^5\right ) \, dx &=-\frac{1}{4 x^4}+\frac{x^2}{2}+\frac{x^6}{6}\\ \end{align*}

Mathematica [A]  time = 0.0012878, size = 22, normalized size = 1. \[ \frac{x^6}{6}+\frac{x^2}{2}-\frac{1}{4 x^4} \]

Antiderivative was successfully verified.

[In]

Integrate[x^(-5) + x + x^5,x]

[Out]

-1/(4*x^4) + x^2/2 + x^6/6

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Maple [A]  time = 0.001, size = 17, normalized size = 0.8 \begin{align*} -{\frac{1}{4\,{x}^{4}}}+{\frac{{x}^{2}}{2}}+{\frac{{x}^{6}}{6}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^5+x+x^5,x)

[Out]

-1/4/x^4+1/2*x^2+1/6*x^6

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Maxima [A]  time = 1.0322, size = 22, normalized size = 1. \begin{align*} \frac{1}{6} \, x^{6} + \frac{1}{2} \, x^{2} - \frac{1}{4 \, x^{4}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^5+x+x^5,x, algorithm="maxima")

[Out]

1/6*x^6 + 1/2*x^2 - 1/4/x^4

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Fricas [A]  time = 1.8937, size = 42, normalized size = 1.91 \begin{align*} \frac{2 \, x^{10} + 6 \, x^{6} - 3}{12 \, x^{4}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^5+x+x^5,x, algorithm="fricas")

[Out]

1/12*(2*x^10 + 6*x^6 - 3)/x^4

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Sympy [A]  time = 0.077435, size = 15, normalized size = 0.68 \begin{align*} \frac{x^{6}}{6} + \frac{x^{2}}{2} - \frac{1}{4 x^{4}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**5+x+x**5,x)

[Out]

x**6/6 + x**2/2 - 1/(4*x**4)

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Giac [A]  time = 1.05989, size = 22, normalized size = 1. \begin{align*} \frac{1}{6} \, x^{6} + \frac{1}{2} \, x^{2} - \frac{1}{4 \, x^{4}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^5+x+x^5,x, algorithm="giac")

[Out]

1/6*x^6 + 1/2*x^2 - 1/4/x^4