Optimal. Leaf size=32 \[ \frac{6 (a+b x)^{5/6}}{5 (c+d x)^{5/6} (b c-a d)} \]
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Rubi [A] time = 0.0031016, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {37} \[ \frac{6 (a+b x)^{5/6}}{5 (c+d x)^{5/6} (b c-a d)} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int \frac{1}{\sqrt [6]{a+b x} (c+d x)^{11/6}} \, dx &=\frac{6 (a+b x)^{5/6}}{5 (b c-a d) (c+d x)^{5/6}}\\ \end{align*}
Mathematica [A] time = 0.0107222, size = 32, normalized size = 1. \[ \frac{6 (a+b x)^{5/6}}{5 (c+d x)^{5/6} (b c-a d)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 27, normalized size = 0.8 \begin{align*} -{\frac{6}{5\,ad-5\,bc} \left ( bx+a \right ) ^{{\frac{5}{6}}} \left ( dx+c \right ) ^{-{\frac{5}{6}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b x + a\right )}^{\frac{1}{6}}{\left (d x + c\right )}^{\frac{11}{6}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.86014, size = 99, normalized size = 3.09 \begin{align*} \frac{6 \,{\left (b x + a\right )}^{\frac{5}{6}}{\left (d x + c\right )}^{\frac{1}{6}}}{5 \,{\left (b c^{2} - a c d +{\left (b c d - a d^{2}\right )} x\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] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b x + a\right )}^{\frac{1}{6}}{\left (d x + c\right )}^{\frac{11}{6}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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