Optimal. Leaf size=37 \[ \frac{1}{6} e^{-2 x} \left (e^{7 x}-3\right )^{5/3} \, _2F_1\left (1,\frac{29}{21};\frac{5}{7};\frac{e^{7 x}}{3}\right ) \]
[Out]
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Rubi [A] time = 0.0941681, antiderivative size = 57, normalized size of antiderivative = 1.54, number of steps used = 4, number of rules used = 4, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.235 \[ -\frac{3^{2/3} e^{-2 x} \left (e^{7 x}-3\right )^{2/3} \, _2F_1\left (-\frac{2}{3},-\frac{2}{7};\frac{5}{7};\frac{e^{7 x}}{3}\right )}{2 \left (3-e^{7 x}\right )^{2/3}} \]
Antiderivative was successfully verified.
[In] Int[(-3 + E^(7*x))^(2/3)/E^(2*x),x]
[Out]
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Rubi in Sympy [A] time = 6.56238, size = 46, normalized size = 1.24 \[ - \frac{\left (e^{7 x} - 3\right )^{\frac{2}{3}} e^{- 2 x}{{}_{2}F_{1}\left (\begin{matrix} - \frac{2}{3}, - \frac{2}{7} \\ \frac{5}{7} \end{matrix}\middle |{\frac{e^{7 x}}{3}} \right )}}{2 \left (- \frac{e^{7 x}}{3} + 1\right )^{\frac{2}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-3+exp(7*x))**(2/3)/exp(2*x),x)
[Out]
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Mathematica [A] time = 0.0560825, size = 68, normalized size = 1.84 \[ \frac{e^{-2 x} \left (7\ 3^{2/3} \sqrt [3]{3-e^{7 x}} \, _2F_1\left (-\frac{2}{7},\frac{1}{3};\frac{5}{7};\frac{e^{7 x}}{3}\right )+3 e^{7 x}-9\right )}{8 \sqrt [3]{e^{7 x}-3}} \]
Antiderivative was successfully verified.
[In] Integrate[(-3 + E^(7*x))^(2/3)/E^(2*x),x]
[Out]
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Maple [F] time = 0.033, size = 0, normalized size = 0. \[ \int{\frac{1}{{{\rm e}^{2\,x}}} \left ( -3+{{\rm e}^{7\,x}} \right ) ^{{\frac{2}{3}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-3+exp(7*x))^(2/3)/exp(2*x),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (e^{\left (7 \, x\right )} - 3\right )}^{\frac{2}{3}} e^{\left (-2 \, x\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e^(7*x) - 3)^(2/3)*e^(-2*x),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left ({\left (e^{\left (7 \, x\right )} - 3\right )}^{\frac{2}{3}} e^{\left (-2 \, x\right )}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e^(7*x) - 3)^(2/3)*e^(-2*x),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \left (e^{7 x} - 3\right )^{\frac{2}{3}} e^{- 2 x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-3+exp(7*x))**(2/3)/exp(2*x),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (e^{\left (7 \, x\right )} - 3\right )}^{\frac{2}{3}} e^{\left (-2 \, x\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e^(7*x) - 3)^(2/3)*e^(-2*x),x, algorithm="giac")
[Out]