Optimal. Leaf size=32 \[ \frac {6 (a+b x)^{5/6}}{5 (b c-a d) (c+d x)^{5/6}} \]
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Rubi [A]
time = 0.00, antiderivative size = 32, normalized size of antiderivative = 1.00, 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}
\begin {gather*} \frac {6 (a+b x)^{5/6}}{5 (c+d x)^{5/6} (b c-a d)} \end {gather*}
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*}
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Mathematica [A]
time = 0.03, size = 32, normalized size = 1.00 \begin {gather*} \frac {6 (a+b x)^{5/6}}{5 (b c-a d) (c+d x)^{5/6}} \end {gather*}
Antiderivative was successfully verified.
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Mathics [F(-1)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Warning: Unable to verify antiderivative.
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Maple [A]
time = 0.19, size = 27, normalized size = 0.84
method | result | size |
gosper | \(-\frac {6 \left (b x +a \right )^{\frac {5}{6}}}{5 \left (d x +c \right )^{\frac {5}{6}} \left (a d -b c \right )}\) | \(27\) |
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 42, normalized size = 1.31 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\sqrt [6]{a + b x} \left (c + d x\right )^{\frac {11}{6}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] N/A
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.76, size = 27, normalized size = 0.84 \begin {gather*} -\frac {6\,{\left (a+b\,x\right )}^{5/6}}{\left (5\,a\,d-5\,b\,c\right )\,{\left (c+d\,x\right )}^{5/6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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