Optimal. Leaf size=18 \[ -5 e^{4/x}-x^3 (10+x) \]
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Rubi [A] time = 0.03, antiderivative size = 20, normalized size of antiderivative = 1.11, number of steps used = 5, number of rules used = 3, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {14, 2209, 43} \begin {gather*} -x^4-10 x^3-5 e^{4/x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 43
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {20 e^{4/x}}{x^2}-2 x^2 (15+2 x)\right ) \, dx\\ &=-\left (2 \int x^2 (15+2 x) \, dx\right )+20 \int \frac {e^{4/x}}{x^2} \, dx\\ &=-5 e^{4/x}-2 \int \left (15 x^2+2 x^3\right ) \, dx\\ &=-5 e^{4/x}-10 x^3-x^4\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 1.11 \begin {gather*} -5 e^{4/x}-10 x^3-x^4 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 19, normalized size = 1.06 \begin {gather*} -x^{4} - 10 \, x^{3} - 5 \, e^{\frac {4}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 23, normalized size = 1.28 \begin {gather*} -x^{4} {\left (\frac {10}{x} + \frac {5 \, e^{\frac {4}{x}}}{x^{4}} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 20, normalized size = 1.11
method | result | size |
derivativedivides | \(-x^{4}-10 x^{3}-5 \,{\mathrm e}^{\frac {4}{x}}\) | \(20\) |
default | \(-x^{4}-10 x^{3}-5 \,{\mathrm e}^{\frac {4}{x}}\) | \(20\) |
risch | \(-x^{4}-10 x^{3}-5 \,{\mathrm e}^{\frac {4}{x}}\) | \(20\) |
norman | \(\frac {-10 x^{4}-x^{5}-5 x \,{\mathrm e}^{\frac {4}{x}}}{x}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 19, normalized size = 1.06 \begin {gather*} -x^{4} - 10 \, x^{3} - 5 \, e^{\frac {4}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.14, size = 19, normalized size = 1.06 \begin {gather*} -5\,{\mathrm {e}}^{4/x}-10\,x^3-x^4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 15, normalized size = 0.83 \begin {gather*} - x^{4} - 10 x^{3} - 5 e^{\frac {4}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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