Optimal. Leaf size=82 \[ \frac {6 b (a+b x)^{7/6} \left (\frac {b (c+d x)}{b c-a d}\right )^{5/6} \, _2F_1\left (\frac {7}{6},\frac {17}{6};\frac {13}{6};-\frac {d (a+b x)}{b c-a d}\right )}{7 (c+d x)^{5/6} (b c-a d)^2} \]
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Rubi [A] time = 0.02, antiderivative size = 82, normalized size of antiderivative = 1.00, 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} \[ \frac {6 b (a+b x)^{7/6} \left (\frac {b (c+d x)}{b c-a d}\right )^{5/6} \, _2F_1\left (\frac {7}{6},\frac {17}{6};\frac {13}{6};-\frac {d (a+b x)}{b c-a d}\right )}{7 (c+d x)^{5/6} (b c-a d)^2} \]
Antiderivative was successfully verified.
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Rule 69
Rule 70
Rubi steps
\begin {align*} \int \frac {\sqrt [6]{a+b x}}{(c+d x)^{17/6}} \, dx &=\frac {\left (b^2 \left (\frac {b (c+d x)}{b c-a d}\right )^{5/6}\right ) \int \frac {\sqrt [6]{a+b x}}{\left (\frac {b c}{b c-a d}+\frac {b d x}{b c-a d}\right )^{17/6}} \, dx}{(b c-a d)^2 (c+d x)^{5/6}}\\ &=\frac {6 b (a+b x)^{7/6} \left (\frac {b (c+d x)}{b c-a d}\right )^{5/6} \, _2F_1\left (\frac {7}{6},\frac {17}{6};\frac {13}{6};-\frac {d (a+b x)}{b c-a d}\right )}{7 (b c-a d)^2 (c+d x)^{5/6}}\\ \end {align*}
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Mathematica [A] time = 0.05, size = 81, normalized size = 0.99 \[ \frac {6 b (a+b x)^{7/6} \left (\frac {b (c+d x)}{b c-a d}\right )^{5/6} \, _2F_1\left (\frac {7}{6},\frac {17}{6};\frac {13}{6};\frac {d (a+b x)}{a d-b c}\right )}{7 (c+d x)^{5/6} (b c-a d)^2} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.71, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (b x + a\right )}^{\frac {1}{6}} {\left (d x + c\right )}^{\frac {1}{6}}}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b x + a\right )}^{\frac {1}{6}}}{{\left (d x + c\right )}^{\frac {17}{6}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.09, size = 0, normalized size = 0.00 \[ \int \frac {\left (b x +a \right )^{\frac {1}{6}}}{\left (d x +c \right )^{\frac {17}{6}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b x + a\right )}^{\frac {1}{6}}}{{\left (d x + c\right )}^{\frac {17}{6}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.01 \[ \int \frac {{\left (a+b\,x\right )}^{1/6}}{{\left (c+d\,x\right )}^{17/6}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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