Optimal. Leaf size=61 \[ \frac {\sqrt {x^{10}+x^8-2 x^5+1} \left (x^5-1\right )}{2 x^8}+\frac {1}{2} \log \left (x^5+\sqrt {x^{10}+x^8-2 x^5+1}-1\right )-2 \log (x) \]
________________________________________________________________________________________
Rubi [F] time = 0.28, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\left (4+x^5\right ) \sqrt {1-2 x^5+x^8+x^{10}}}{x^9} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\left (4+x^5\right ) \sqrt {1-2 x^5+x^8+x^{10}}}{x^9} \, dx &=\int \left (\frac {4 \sqrt {1-2 x^5+x^8+x^{10}}}{x^9}+\frac {\sqrt {1-2 x^5+x^8+x^{10}}}{x^4}\right ) \, dx\\ &=4 \int \frac {\sqrt {1-2 x^5+x^8+x^{10}}}{x^9} \, dx+\int \frac {\sqrt {1-2 x^5+x^8+x^{10}}}{x^4} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [F] time = 0.19, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (4+x^5\right ) \sqrt {1-2 x^5+x^8+x^{10}}}{x^9} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.33, size = 61, normalized size = 1.00 \begin {gather*} \frac {\left (-1+x^5\right ) \sqrt {1-2 x^5+x^8+x^{10}}}{2 x^8}-2 \log (x)+\frac {1}{2} \log \left (-1+x^5+\sqrt {1-2 x^5+x^8+x^{10}}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt {x^{10} + x^{8} - 2 \, x^{5} + 1} {\left (x^{5} + 4\right )}}{x^{9}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.77, size = 67, normalized size = 1.10
method | result | size |
trager | \(\frac {\left (-1+x \right ) \left (x^{4}+x^{3}+x^{2}+x +1\right ) \sqrt {x^{10}+x^{8}-2 x^{5}+1}}{2 x^{8}}-\frac {\ln \left (-\frac {-x^{5}+\sqrt {x^{10}+x^{8}-2 x^{5}+1}+1}{x^{4}}\right )}{2}\) | \(67\) |
risch | \(\frac {x^{15}+x^{13}-3 x^{10}-x^{8}+3 x^{5}-1}{2 x^{8} \sqrt {x^{10}+x^{8}-2 x^{5}+1}}+\frac {\ln \left (-\frac {-1+x^{5}+\sqrt {x^{10}+x^{8}-2 x^{5}+1}}{x^{4}}\right )}{2}\) | \(73\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt {x^{10} + x^{8} - 2 \, x^{5} + 1} {\left (x^{5} + 4\right )}}{x^{9}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.02 \begin {gather*} \int \frac {\left (x^5+4\right )\,\sqrt {x^{10}+x^8-2\,x^5+1}}{x^9} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (x^{5} + 4\right ) \sqrt {x^{10} + x^{8} - 2 x^{5} + 1}}{x^{9}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________