Optimal. Leaf size=32 \[ \frac {6 (a+b x)^{11/6}}{11 (c+d x)^{11/6} (b c-a d)} \]
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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} \[ \frac {6 (a+b x)^{11/6}}{11 (c+d x)^{11/6} (b c-a d)} \]
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 = 0.01, size = 32, normalized size = 1.00 \[ \frac {6 (a+b x)^{11/6}}{11 (c+d x)^{11/6} (b c-a d)} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.79, size = 65, normalized size = 2.03 \[ \frac {6 \, {\left (b x + a\right )}^{\frac {11}{6}} {\left (d x + c\right )}^{\frac {1}{6}}}{11 \, {\left (b c^{3} - a c^{2} d + {\left (b c d^{2} - a d^{3}\right )} x^{2} + 2 \, {\left (b c^{2} d - a c d^{2}\right )} x\right )}} \]
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 \[ \int \frac {{\left (b x + a\right )}^{\frac {5}{6}}}{{\left (d x + c\right )}^{\frac {17}{6}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 27, normalized size = 0.84 \[ -\frac {6 \left (b x +a \right )^{\frac {11}{6}}}{11 \left (d x +c \right )^{\frac {11}{6}} \left (a d -b c \right )} \]
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 \[ \int \frac {{\left (b x + a\right )}^{\frac {5}{6}}}{{\left (d x + c\right )}^{\frac {17}{6}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.59, size = 130, normalized size = 4.06 \[ -\frac {\left (\frac {6\,a\,{\left (a+b\,x\right )}^{5/6}}{11\,a\,d^3-11\,b\,c\,d^2}+\frac {6\,b\,x\,{\left (a+b\,x\right )}^{5/6}}{11\,a\,d^3-11\,b\,c\,d^2}\right )\,{\left (c+d\,x\right )}^{1/6}}{x^2-\frac {11\,b\,c^3-11\,a\,c^2\,d}{11\,a\,d^3-11\,b\,c\,d^2}+\frac {22\,c\,d\,x\,\left (a\,d-b\,c\right )}{11\,a\,d^3-11\,b\,c\,d^2}} \]
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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