Optimal. Leaf size=22 \[ 6-\frac {3}{x+\frac {3}{-\frac {5}{8}+49 e^x x}} \]
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Rubi [F]
time = 1.01, 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 {75+e^x (-28224-39984 x)+460992 e^{2 x} x^2}{576-240 x+25 x^2+153664 e^{2 x} x^4+e^x \left (18816 x^2-3920 x^3\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {75+460992 e^{2 x} x^2-2352 e^x (12+17 x)}{\left (24-5 x+392 e^x x^2\right )^2} \, dx\\ &=\int \left (\frac {3}{x^2}-\frac {72 \left (-48-19 x+5 x^2\right )}{x^2 \left (24-5 x+392 e^x x^2\right )^2}-\frac {72 (3+x)}{x^2 \left (24-5 x+392 e^x x^2\right )}\right ) \, dx\\ &=-\frac {3}{x}-72 \int \frac {-48-19 x+5 x^2}{x^2 \left (24-5 x+392 e^x x^2\right )^2} \, dx-72 \int \frac {3+x}{x^2 \left (24-5 x+392 e^x x^2\right )} \, dx\\ &=-\frac {3}{x}-72 \int \left (\frac {5}{\left (24-5 x+392 e^x x^2\right )^2}-\frac {48}{x^2 \left (24-5 x+392 e^x x^2\right )^2}-\frac {19}{x \left (24-5 x+392 e^x x^2\right )^2}\right ) \, dx-72 \int \left (\frac {3}{x^2 \left (24-5 x+392 e^x x^2\right )}+\frac {1}{x \left (24-5 x+392 e^x x^2\right )}\right ) \, dx\\ &=-\frac {3}{x}-72 \int \frac {1}{x \left (24-5 x+392 e^x x^2\right )} \, dx-216 \int \frac {1}{x^2 \left (24-5 x+392 e^x x^2\right )} \, dx-360 \int \frac {1}{\left (24-5 x+392 e^x x^2\right )^2} \, dx+1368 \int \frac {1}{x \left (24-5 x+392 e^x x^2\right )^2} \, dx+3456 \int \frac {1}{x^2 \left (24-5 x+392 e^x x^2\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 1.64, size = 26, normalized size = 1.18 \begin {gather*} -\frac {3}{x}+\frac {72}{x \left (24-5 x+392 e^x x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 23, normalized size = 1.05
method | result | size |
norman | \(\frac {15-1176 \,{\mathrm e}^{x} x}{392 \,{\mathrm e}^{x} x^{2}-5 x +24}\) | \(23\) |
risch | \(-\frac {3}{x}+\frac {72}{x \left (392 \,{\mathrm e}^{x} x^{2}-5 x +24\right )}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 23, normalized size = 1.05 \begin {gather*} -\frac {3 \, {\left (392 \, x e^{x} - 5\right )}}{392 \, x^{2} e^{x} - 5 \, x + 24} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 23, normalized size = 1.05 \begin {gather*} -\frac {3 \, {\left (392 \, x e^{x} - 5\right )}}{392 \, x^{2} e^{x} - 5 \, x + 24} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 20, normalized size = 0.91 \begin {gather*} \frac {72}{392 x^{3} e^{x} - 5 x^{2} + 24 x} - \frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 23, normalized size = 1.05 \begin {gather*} -\frac {3 \, {\left (392 \, x e^{x} - 5\right )}}{392 \, x^{2} e^{x} - 5 \, x + 24} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.14, size = 23, normalized size = 1.05 \begin {gather*} -\frac {1176\,x\,{\mathrm {e}}^x-15}{392\,x^2\,{\mathrm {e}}^x-5\,x+24} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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