Optimal. Leaf size=30 \[ 4 e^{\sqrt [4]{x}} \left (-6+6 \sqrt [4]{x}-3 \sqrt {x}+x^{3/4}\right ) \]
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Rubi [A]
time = 0.02, antiderivative size = 52, normalized size of antiderivative = 1.73, number of steps
used = 5, number of rules used = 3, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.429, Rules used = {2238, 2207,
2225} \begin {gather*} 4 e^{\sqrt [4]{x}} x^{3/4}-12 e^{\sqrt [4]{x}} \sqrt {x}+24 e^{\sqrt [4]{x}} \sqrt [4]{x}-24 e^{\sqrt [4]{x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2207
Rule 2225
Rule 2238
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=4 \text {Subst}\left (\int e^x x^3 \, dx,x,\sqrt [4]{x}\right )\\ &=4 e^{\sqrt [4]{x}} x^{3/4}-12 \text {Subst}\left (\int e^x x^2 \, dx,x,\sqrt [4]{x}\right )\\ &=-12 e^{\sqrt [4]{x}} \sqrt {x}+4 e^{\sqrt [4]{x}} x^{3/4}+24 \text {Subst}\left (\int e^x x \, dx,x,\sqrt [4]{x}\right )\\ &=24 e^{\sqrt [4]{x}} \sqrt [4]{x}-12 e^{\sqrt [4]{x}} \sqrt {x}+4 e^{\sqrt [4]{x}} x^{3/4}-24 \text {Subst}\left (\int e^x \, dx,x,\sqrt [4]{x}\right )\\ &=-24 e^{\sqrt [4]{x}}+24 e^{\sqrt [4]{x}} \sqrt [4]{x}-12 e^{\sqrt [4]{x}} \sqrt {x}+4 e^{\sqrt [4]{x}} x^{3/4}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 31, normalized size = 1.03 \begin {gather*} e^{\sqrt [4]{x}} \left (-24+24 \sqrt [4]{x}-12 \sqrt {x}+4 x^{3/4}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 35, normalized size = 1.17
method | result | size |
meijerg | \(24-\left (-4 x^{\frac {3}{4}}+12 \sqrt {x}-24 x^{\frac {1}{4}}+24\right ) {\mathrm e}^{x^{\frac {1}{4}}}\) | \(26\) |
derivativedivides | \(4 \,{\mathrm e}^{x^{\frac {1}{4}}} x^{\frac {3}{4}}-12 \sqrt {x}\, {\mathrm e}^{x^{\frac {1}{4}}}+24 x^{\frac {1}{4}} {\mathrm e}^{x^{\frac {1}{4}}}-24 \,{\mathrm e}^{x^{\frac {1}{4}}}\) | \(35\) |
default | \(4 \,{\mathrm e}^{x^{\frac {1}{4}}} x^{\frac {3}{4}}-12 \sqrt {x}\, {\mathrm e}^{x^{\frac {1}{4}}}+24 x^{\frac {1}{4}} {\mathrm e}^{x^{\frac {1}{4}}}-24 \,{\mathrm e}^{x^{\frac {1}{4}}}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 21, normalized size = 0.70 \begin {gather*} 4 \, {\left (x^{\frac {3}{4}} - 3 \, \sqrt {x} + 6 \, x^{\frac {1}{4}} - 6\right )} e^{\left (x^{\frac {1}{4}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.57, size = 21, normalized size = 0.70 \begin {gather*} 4 \, {\left (x^{\frac {3}{4}} - 3 \, \sqrt {x} + 6 \, x^{\frac {1}{4}} - 6\right )} e^{\left (x^{\frac {1}{4}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.18, size = 48, normalized size = 1.60 \begin {gather*} 4 x^{\frac {3}{4}} e^{\sqrt [4]{x}} + 24 \sqrt [4]{x} e^{\sqrt [4]{x}} - 12 \sqrt {x} e^{\sqrt [4]{x}} - 24 e^{\sqrt [4]{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 21, normalized size = 0.70 \begin {gather*} 4 \, {\left (x^{\frac {3}{4}} - 3 \, \sqrt {x} + 6 \, x^{\frac {1}{4}} - 6\right )} e^{\left (x^{\frac {1}{4}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 28, normalized size = 0.93 \begin {gather*} -4\,x\,{\mathrm {e}}^{x^{1/4}}\,\left (\frac {6}{x}+\frac {3}{\sqrt {x}}-\frac {1}{x^{1/4}}-\frac {6}{x^{3/4}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F] Failed to verify
time = 1.00, size = 9, normalized size = 0.30 \begin {gather*} \frac {4 x^{\frac {3}{4}} {\mathrm e}^{x^{\frac {1}{4}}}}{3} \end {gather*}
Warning: Unable to verify antiderivative.
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