3.20.6 \(\int (-\frac {1}{7 x^6}+x^6) \, dx\) [1906]

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

[Out]

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

________________________________________________________________________________________

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 = {} \begin {gather*} \frac {x^7}{7}+\frac {1}{35 x^5} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1/7*1/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 = 0.00, size = 15, normalized size = 1.00 \begin {gather*} \frac {1}{35 x^5}+\frac {x^7}{7} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1/7*1/x^6 + x^6,x]

[Out]

1/(35*x^5) + x^7/7

________________________________________________________________________________________

Maple [A]
time = 0.02, size = 12, normalized size = 0.80

method	result	size
default	\(\frac {1}{35 x^{5}}+\frac {x^{7}}{7}\)	\(12\)
norman	\(\frac {\frac {1}{35}+\frac {x^{12}}{7}}{x^{5}}\)	\(12\)
risch	\(\frac {1}{35 x^{5}}+\frac {x^{7}}{7}\)	\(12\)
gosper	\(\frac {5 x^{12}+1}{35 x^{5}}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

Maxima [A]
time = 0.28, size = 11, normalized size = 0.73 \begin {gather*} \frac {1}{7} \, x^{7} + \frac {1}{35 \, x^{5}} \end {gather*}

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

________________________________________________________________________________________

Fricas [A]
time = 0.61, size = 12, normalized size = 0.80 \begin {gather*} \frac {5 \, x^{12} + 1}{35 \, x^{5}} \end {gather*}

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

________________________________________________________________________________________

Sympy [A]
time = 0.02, size = 10, normalized size = 0.67 \begin {gather*} \frac {x^{7}}{7} + \frac {1}{35 x^{5}} \end {gather*}

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)

________________________________________________________________________________________

Giac [A]
time = 1.55, size = 11, normalized size = 0.73 \begin {gather*} \frac {1}{7} \, x^{7} + \frac {1}{35 \, x^{5}} \end {gather*}

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

________________________________________________________________________________________

Mupad [B]
time = 0.03, size = 12, normalized size = 0.80 \begin {gather*} \frac {5\,x^{12}+1}{35\,x^5} \end {gather*}

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)

________________________________________________________________________________________