\(\int (\frac {1}{x^5}+x+x^5) \, dx\) [1903]

Optimal result

Integrand size = 8, antiderivative size = 22 \[ \int \left (\frac {1}{x^5}+x+x^5\right ) \, dx=-\frac {1}{4 x^4}+\frac {x^2}{2}+\frac {x^6}{6} \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 22, 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 = {} \[ \int \left (\frac {1}{x^5}+x+x^5\right ) \, dx=\frac {x^6}{6}-\frac {1}{4 x^4}+\frac {x^2}{2} \]

[In]

Int[x^(-5) + x + x^5,x]

[Out]

-1/4*1/x^4 + x^2/2 + x^6/6

Rubi steps \begin{align*} \text {integral}& = -\frac {1}{4 x^4}+\frac {x^2}{2}+\frac {x^6}{6} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \left (\frac {1}{x^5}+x+x^5\right ) \, dx=-\frac {1}{4 x^4}+\frac {x^2}{2}+\frac {x^6}{6} \]

[In]

Integrate[x^(-5) + x + x^5,x]

[Out]

-1/4*1/x^4 + x^2/2 + x^6/6

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.77

method	result	size
default	\(-\frac {1}{4 x^{4}}+\frac {x^{2}}{2}+\frac {x^{6}}{6}\)	\(17\)
norman	\(\frac {\frac {1}{6} x^{10}+\frac {1}{2} x^{6}-\frac {1}{4}}{x^{4}}\)	\(17\)
risch	\(-\frac {1}{4 x^{4}}+\frac {x^{2}}{2}+\frac {x^{6}}{6}\)	\(17\)
gosper	\(\frac {2 x^{10}+6 x^{6}-3}{12 x^{4}}\)	\(18\)
parallelrisch	\(\frac {2 x^{10}+6 x^{6}-3}{12 x^{4}}\)	\(18\)

[In]

int(1/x^5+x+x^5,x,method=_RETURNVERBOSE)

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.77 \[ \int \left (\frac {1}{x^5}+x+x^5\right ) \, dx=\frac {2 \, x^{10} + 6 \, x^{6} - 3}{12 \, x^{4}} \]

[In]

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

[Out]

1/12*(2*x^10 + 6*x^6 - 3)/x^4

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.68 \[ \int \left (\frac {1}{x^5}+x+x^5\right ) \, dx=\frac {x^{6}}{6} + \frac {x^{2}}{2} - \frac {1}{4 x^{4}} \]

[In]

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

[Out]

x**6/6 + x**2/2 - 1/(4*x**4)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.73 \[ \int \left (\frac {1}{x^5}+x+x^5\right ) \, dx=\frac {1}{6} \, x^{6} + \frac {1}{2} \, x^{2} - \frac {1}{4 \, x^{4}} \]

[In]

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

[Out]

1/6*x^6 + 1/2*x^2 - 1/4/x^4

Giac [A] (verification not implemented)

none

Time = 0.32 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.73 \[ \int \left (\frac {1}{x^5}+x+x^5\right ) \, dx=\frac {1}{6} \, x^{6} + \frac {1}{2} \, x^{2} - \frac {1}{4 \, x^{4}} \]

[In]

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

[Out]

1/6*x^6 + 1/2*x^2 - 1/4/x^4

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.77 \[ \int \left (\frac {1}{x^5}+x+x^5\right ) \, dx=\frac {2\,x^{10}+6\,x^6-3}{12\,x^4} \]

[In]

int(x + 1/x^5 + x^5,x)

[Out]

(6*x^6 + 2*x^10 - 3)/(12*x^4)