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

Optimal result

Integrand size = 11, antiderivative size = 15 \[ \int \left (-\frac {1}{7 x^6}+x^6\right ) \, dx=\frac {1}{35 x^5}+\frac {x^7}{7} \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (-\frac {1}{7 x^6}+x^6\right ) \, dx=\frac {x^7}{7}+\frac {1}{35 x^5} \]

[In]

Int[-1/7*1/x^6 + x^6,x]

[Out]

1/(35*x^5) + x^7/7

Rubi steps \begin{align*} \text {integral}& = \frac {1}{35 x^5}+\frac {x^7}{7} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \left (-\frac {1}{7 x^6}+x^6\right ) \, dx=\frac {1}{35 x^5}+\frac {x^7}{7} \]

[In]

Integrate[-1/7*1/x^6 + x^6,x]

[Out]

1/(35*x^5) + x^7/7

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 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	\(\frac {5 x^{12}+1}{35 x^{5}}\)	\(13\)
parallelrisch	\(\frac {5 x^{12}+1}{35 x^{5}}\)	\(13\)

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int \left (-\frac {1}{7 x^6}+x^6\right ) \, dx=\frac {5 \, x^{12} + 1}{35 \, x^{5}} \]

[In]

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

[Out]

1/35*(5*x^12 + 1)/x^5

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int \left (-\frac {1}{7 x^6}+x^6\right ) \, dx=\frac {x^{7}}{7} + \frac {1}{35 x^{5}} \]

[In]

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

[Out]

x**7/7 + 1/(35*x**5)

Maxima [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int \left (-\frac {1}{7 x^6}+x^6\right ) \, dx=\frac {1}{7} \, x^{7} + \frac {1}{35 \, x^{5}} \]

[In]

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

[Out]

1/7*x^7 + 1/35/x^5

Giac [A] (verification not implemented)

none

Time = 0.30 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int \left (-\frac {1}{7 x^6}+x^6\right ) \, dx=\frac {1}{7} \, x^{7} + \frac {1}{35 \, x^{5}} \]

[In]

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

[Out]

1/7*x^7 + 1/35/x^5

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int \left (-\frac {1}{7 x^6}+x^6\right ) \, dx=\frac {5\,x^{12}+1}{35\,x^5} \]

[In]

int(x^6 - 1/(7*x^6),x)

[Out]

(5*x^12 + 1)/(35*x^5)