3.1906 \(\int (-\frac{1}{7 x^6}+x^6) \, dx\)

Optimal. Leaf size=15 \[ \frac{x^7}{7}+\frac{1}{35 x^5} \]

[Out]

1/(35*x^5) + x^7/7

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Rubi [A]  time = 0.0018043, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{x^7}{7}+\frac{1}{35 x^5} \]

Antiderivative was successfully verified.

[In]

Int[-1/(7*x^6) + x^6,x]

[Out]

1/(35*x^5) + x^7/7

Rubi steps

\begin{align*} \int \left (-\frac{1}{7 x^6}+x^6\right ) \, dx &=\frac{1}{35 x^5}+\frac{x^7}{7}\\ \end{align*}

Mathematica [A]  time = 0.0013016, size = 15, normalized size = 1. \[ \frac{x^7}{7}+\frac{1}{35 x^5} \]

Antiderivative was successfully verified.

[In]

Integrate[-1/(7*x^6) + x^6,x]

[Out]

1/(35*x^5) + x^7/7

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Maple [A]  time = 0.002, size = 12, normalized size = 0.8 \begin{align*}{\frac{1}{35\,{x}^{5}}}+{\frac{{x}^{7}}{7}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/7/x^6+x^6,x)

[Out]

1/35/x^5+1/7*x^7

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Maxima [A]  time = 0.956039, size = 15, normalized size = 1. \begin{align*} \frac{1}{7} \, x^{7} + \frac{1}{35 \, x^{5}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/7/x^6+x^6,x, algorithm="maxima")

[Out]

1/7*x^7 + 1/35/x^5

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Fricas [A]  time = 1.8777, size = 31, normalized size = 2.07 \begin{align*} \frac{5 \, x^{12} + 1}{35 \, x^{5}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/7/x^6+x^6,x, algorithm="fricas")

[Out]

1/35*(5*x^12 + 1)/x^5

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Sympy [A]  time = 0.080995, size = 10, normalized size = 0.67 \begin{align*} \frac{x^{7}}{7} + \frac{1}{35 x^{5}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/7/x**6+x**6,x)

[Out]

x**7/7 + 1/(35*x**5)

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Giac [A]  time = 1.05916, size = 15, normalized size = 1. \begin{align*} \frac{1}{7} \, x^{7} + \frac{1}{35 \, x^{5}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/7/x^6+x^6,x, algorithm="giac")

[Out]

1/7*x^7 + 1/35/x^5