Optimal. Leaf size=82 \[ \frac{6 (a+b x)^{5/6} (c+d x)^{5/6} (b c-a d) \, _2F_1\left (-\frac{11}{6},\frac{5}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right )}{5 b^2 \left (\frac{b (c+d x)}{b c-a d}\right )^{5/6}} \]
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Rubi [A] time = 0.0235723, antiderivative size = 82, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105, Rules used = {70, 69} \[ \frac{6 (a+b x)^{5/6} (c+d x)^{5/6} (b c-a d) \, _2F_1\left (-\frac{11}{6},\frac{5}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right )}{5 b^2 \left (\frac{b (c+d x)}{b c-a d}\right )^{5/6}} \]
Antiderivative was successfully verified.
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Rule 70
Rule 69
Rubi steps
\begin{align*} \int \frac{(c+d x)^{11/6}}{\sqrt [6]{a+b x}} \, dx &=\frac{\left ((b c-a d) (c+d x)^{5/6}\right ) \int \frac{\left (\frac{b c}{b c-a d}+\frac{b d x}{b c-a d}\right )^{11/6}}{\sqrt [6]{a+b x}} \, dx}{b \left (\frac{b (c+d x)}{b c-a d}\right )^{5/6}}\\ &=\frac{6 (b c-a d) (a+b x)^{5/6} (c+d x)^{5/6} \, _2F_1\left (-\frac{11}{6},\frac{5}{6};\frac{11}{6};-\frac{d (a+b x)}{b c-a d}\right )}{5 b^2 \left (\frac{b (c+d x)}{b c-a d}\right )^{5/6}}\\ \end{align*}
Mathematica [A] time = 0.0498552, size = 73, normalized size = 0.89 \[ \frac{6 (a+b x)^{5/6} (c+d x)^{11/6} \, _2F_1\left (-\frac{11}{6},\frac{5}{6};\frac{11}{6};\frac{d (a+b x)}{a d-b c}\right )}{5 b \left (\frac{b (c+d x)}{b c-a d}\right )^{11/6}} \]
Antiderivative was successfully verified.
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Maple [F] time = 0.034, size = 0, normalized size = 0. \begin{align*} \int{ \left ( dx+c \right ) ^{{\frac{11}{6}}}{\frac{1}{\sqrt [6]{bx+a}}}}\, dx \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{{\left (d x + c\right )}^{\frac{11}{6}}}{{\left (b x + a\right )}^{\frac{1}{6}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{{\left (d x + c\right )}^{\frac{11}{6}}}{{\left (b x + a\right )}^{\frac{1}{6}}}, 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(-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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