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+1/7*x^7

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Rubi [A]  time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, 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*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 1.00 \[ \frac {x^7}{7}+\frac {1}{35 x^5} \]

Antiderivative was successfully verified.

[In]

Integrate[-1/7*1/x^6 + x^6,x]

[Out]

1/(35*x^5) + x^7/7

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fricas [A]  time = 0.43, size = 12, normalized size = 0.80 \[ \frac {5 \, x^{12} + 1}{35 \, x^{5}} \]

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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giac [A]  time = 1.08, size = 11, normalized size = 0.73 \[ \frac {1}{7} \, x^{7} + \frac {1}{35 \, x^{5}} \]

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

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maple [A]  time = 0.00, size = 12, normalized size = 0.80 \[ \frac {x^{7}}{7}+\frac {1}{35 x^{5}} \]

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 = 0.97, size = 11, normalized size = 0.73 \[ \frac {1}{7} \, x^{7} + \frac {1}{35 \, x^{5}} \]

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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mupad [B]  time = 0.03, size = 12, normalized size = 0.80 \[ \frac {5\,x^{12}+1}{35\,x^5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^6 - 1/(7*x^6),x)

[Out]

(5*x^12 + 1)/(35*x^5)

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sympy [A]  time = 0.08, size = 10, normalized size = 0.67 \[ \frac {x^{7}}{7} + \frac {1}{35 x^{5}} \]

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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