Optimal. Leaf size=34 \[ \frac{x^{10}}{10 b}-\frac{2 x^5}{5 b}+\frac{4 \log \left (x^5+2\right )}{5 b} \]
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Rubi [A] time = 0.0198526, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {266, 43} \[ \frac{x^{10}}{10 b}-\frac{2 x^5}{5 b}+\frac{4 \log \left (x^5+2\right )}{5 b} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^{14}}{2 b+b x^5} \, dx &=\frac{1}{5} \operatorname{Subst}\left (\int \frac{x^2}{2 b+b x} \, dx,x,x^5\right )\\ &=\frac{1}{5} \operatorname{Subst}\left (\int \left (-\frac{2}{b}+\frac{x}{b}+\frac{4}{b (2+x)}\right ) \, dx,x,x^5\right )\\ &=-\frac{2 x^5}{5 b}+\frac{x^{10}}{10 b}+\frac{4 \log \left (2+x^5\right )}{5 b}\\ \end{align*}
Mathematica [A] time = 0.006258, size = 25, normalized size = 0.74 \[ \frac{x^{10}-4 x^5+8 \log \left (x^5+2\right )-12}{10 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 29, normalized size = 0.9 \begin{align*} -{\frac{2\,{x}^{5}}{5\,b}}+{\frac{{x}^{10}}{10\,b}}+{\frac{4\,\ln \left ({x}^{5}+2 \right ) }{5\,b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02753, size = 35, normalized size = 1.03 \begin{align*} \frac{x^{10} - 4 \, x^{5}}{10 \, b} + \frac{4 \, \log \left (x^{5} + 2\right )}{5 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.90906, size = 54, normalized size = 1.59 \begin{align*} \frac{x^{10} - 4 \, x^{5} + 8 \, \log \left (x^{5} + 2\right )}{10 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.181778, size = 26, normalized size = 0.76 \begin{align*} \frac{x^{10}}{10 b} - \frac{2 x^{5}}{5 b} + \frac{4 \log{\left (x^{5} + 2 \right )}}{5 b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.22468, size = 41, normalized size = 1.21 \begin{align*} \frac{4 \, \log \left ({\left | x^{5} + 2 \right |}\right )}{5 \, b} + \frac{b x^{10} - 4 \, b x^{5}}{10 \, b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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