Optimal. Leaf size=11 \[ x^{10} \cos \left (x^5 \log (x)\right ) \]
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Rubi [F] time = 0.275911, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \left (10 x^9 \cos \left (x^5 \log (x)\right )-x^{10} \left (x^4+5 x^4 \log (x)\right ) \sin \left (x^5 \log (x)\right )\right ) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \left (10 x^9 \cos \left (x^5 \log (x)\right )-x^{10} \left (x^4+5 x^4 \log (x)\right ) \sin \left (x^5 \log (x)\right )\right ) \, dx &=10 \int x^9 \cos \left (x^5 \log (x)\right ) \, dx-\int x^{10} \left (x^4+5 x^4 \log (x)\right ) \sin \left (x^5 \log (x)\right ) \, dx\\ &=10 \int x^9 \cos \left (x^5 \log (x)\right ) \, dx-\int x^{14} (1+5 \log (x)) \sin \left (x^5 \log (x)\right ) \, dx\\ &=10 \int x^9 \cos \left (x^5 \log (x)\right ) \, dx-\int \left (x^{14} \sin \left (x^5 \log (x)\right )+5 x^{14} \log (x) \sin \left (x^5 \log (x)\right )\right ) \, dx\\ &=-\left (5 \int x^{14} \log (x) \sin \left (x^5 \log (x)\right ) \, dx\right )+10 \int x^9 \cos \left (x^5 \log (x)\right ) \, dx-\int x^{14} \sin \left (x^5 \log (x)\right ) \, dx\\ \end{align*}
Mathematica [A] time = 0.319045, size = 11, normalized size = 1. \[ x^{10} \cos \left (x^5 \log (x)\right ) \]
Antiderivative was successfully verified.
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Maple [C] time = 0.109, size = 30, normalized size = 2.7 \begin{align*}{\frac{{x}^{10}{x}^{i{x}^{5}}}{2}}+{\frac{{x}^{10}}{2\,{x}^{i{x}^{5}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.20728, size = 15, normalized size = 1.36 \begin{align*} x^{10} \cos \left (x^{5} \log \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.15781, size = 30, normalized size = 2.73 \begin{align*} x^{10} \cos \left (x^{5} \log \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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