Optimal. Leaf size=25 \[ \frac {x^{10}}{10}-\frac {x^5}{5}+\frac {1}{5} \log \left (x^5+1\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {266, 43} \[ \frac {x^{10}}{10}-\frac {x^5}{5}+\frac {1}{5} \log \left (x^5+1\right ) \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {x^{14}}{1+x^5} \, dx &=\frac {1}{5} \operatorname {Subst}\left (\int \frac {x^2}{1+x} \, dx,x,x^5\right )\\ &=\frac {1}{5} \operatorname {Subst}\left (\int \left (-1+x+\frac {1}{1+x}\right ) \, dx,x,x^5\right )\\ &=-\frac {x^5}{5}+\frac {x^{10}}{10}+\frac {1}{5} \log \left (1+x^5\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 0.88 \[ \frac {1}{10} \left (x^{10}-2 x^5+2 \log \left (x^5+1\right )-3\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 19, normalized size = 0.76 \[ \frac {1}{10} \, x^{10} - \frac {1}{5} \, x^{5} + \frac {1}{5} \, \log \left (x^{5} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 20, normalized size = 0.80 \[ \frac {1}{10} \, x^{10} - \frac {1}{5} \, x^{5} + \frac {1}{5} \, \log \left ({\left | x^{5} + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 20, normalized size = 0.80 \[ \frac {x^{10}}{10}-\frac {x^{5}}{5}+\frac {\ln \left (x^{5}+1\right )}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.08, size = 19, normalized size = 0.76 \[ \frac {1}{10} \, x^{10} - \frac {1}{5} \, x^{5} + \frac {1}{5} \, \log \left (x^{5} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 19, normalized size = 0.76 \[ \frac {\ln \left (x^5+1\right )}{5}-\frac {x^5}{5}+\frac {x^{10}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 17, normalized size = 0.68 \[ \frac {x^{10}}{10} - \frac {x^{5}}{5} + \frac {\log {\left (x^{5} + 1 \right )}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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