Optimal. Leaf size=32 \[ \frac {6 (a+b x)^{11/6}}{11 (b c-a d) (c+d x)^{11/6}} \]
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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)^{11/6}}{11 (c+d x)^{11/6} (b c-a d)} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {(a+b x)^{5/6}}{(c+d x)^{17/6}} \, dx &=\frac {6 (a+b x)^{11/6}}{11 (b c-a d) (c+d x)^{11/6}}\\ \end {align*}
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Mathematica [A]
time = 0.05, size = 32, normalized size = 1.00 \begin {gather*} \frac {6 (a+b x)^{11/6}}{11 (b c-a d) (c+d x)^{11/6}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.18, size = 27, normalized size = 0.84
method | result | size |
gosper | \(-\frac {6 \left (b x +a \right )^{\frac {11}{6}}}{11 \left (d x +c \right )^{\frac {11}{6}} \left (a d -b c \right )}\) | \(27\) |
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 [B] Leaf count of result is larger than twice the leaf count of optimal. 65 vs.
\(2 (26) = 52\).
time = 1.02, size = 65, normalized size = 2.03 \begin {gather*} \frac {6 \, {\left (b x + a\right )}^{\frac {11}{6}} {\left (d x + c\right )}^{\frac {1}{6}}}{11 \, {\left (b c^{3} - a c^{2} d + {\left (b c d^{2} - a d^{3}\right )} x^{2} + 2 \, {\left (b c^{2} d - a c d^{2}\right )} x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \end {gather*}
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 \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 = 0.59, size = 130, normalized size = 4.06 \begin {gather*} -\frac {\left (\frac {6\,a\,{\left (a+b\,x\right )}^{5/6}}{11\,a\,d^3-11\,b\,c\,d^2}+\frac {6\,b\,x\,{\left (a+b\,x\right )}^{5/6}}{11\,a\,d^3-11\,b\,c\,d^2}\right )\,{\left (c+d\,x\right )}^{1/6}}{x^2-\frac {11\,b\,c^3-11\,a\,c^2\,d}{11\,a\,d^3-11\,b\,c\,d^2}+\frac {22\,c\,d\,x\,\left (a\,d-b\,c\right )}{11\,a\,d^3-11\,b\,c\,d^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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