Optimal. Leaf size=32 \[ \text {Int}\left (\frac {\sqrt [3]{a+b \sec (e+f x)}}{(c+d \sec (e+f x))^{7/3}},x\right ) \]
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Rubi [A]
time = 0.06, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {\sqrt [3]{a+b \sec (e+f x)}}{(c+d \sec (e+f x))^{7/3}} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\sqrt [3]{a+b \sec (e+f x)}}{(c+d \sec (e+f x))^{7/3}} \, dx &=\int \frac {\sqrt [3]{a+b \sec (e+f x)}}{(c+d \sec (e+f x))^{7/3}} \, dx\\ \end {align*}
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Mathematica [A]
time = 78.30, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt [3]{a+b \sec (e+f x)}}{(c+d \sec (e+f x))^{7/3}} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.15, size = 0, normalized size = 0.00 \[\int \frac {\left (a +b \sec \left (f x +e \right )\right )^{\frac {1}{3}}}{\left (c +d \sec \left (f x +e \right )\right )^{\frac {7}{3}}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
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 [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \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 [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 [F(-1)]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \text {Hanged} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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