Optimal. Leaf size=16 \[ -1+\frac {4}{e-x}+\frac {34 x}{5} \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.94, number of steps used = 4, number of rules used = 3, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.088, Rules used = {27, 12, 683} \begin {gather*} \frac {34 x}{5}+\frac {4}{e-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 683
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {20+34 e^2-68 e x+34 x^2}{5 (e-x)^2} \, dx\\ &=\frac {1}{5} \int \frac {20+34 e^2-68 e x+34 x^2}{(e-x)^2} \, dx\\ &=\frac {1}{5} \int \left (34+\frac {20}{(e-x)^2}\right ) \, dx\\ &=\frac {4}{e-x}+\frac {34 x}{5}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.31 \begin {gather*} \frac {2}{5} \left (\frac {10}{e-x}-17 (e-x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.10, size = 22, normalized size = 1.38 \begin {gather*} \frac {2 \, {\left (17 \, x^{2} - 17 \, x e - 10\right )}}{5 \, {\left (x - e\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: NotImplementedError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.35, size = 15, normalized size = 0.94
method | result | size |
risch | \(\frac {34 x}{5}+\frac {4}{{\mathrm e}-x}\) | \(15\) |
norman | \(\frac {-\frac {34 x^{2}}{5}+4+\frac {34 \,{\mathrm e}^{2}}{5}}{{\mathrm e}-x}\) | \(23\) |
gosper | \(\frac {-\frac {34 x^{2}}{5}+4+\frac {34 \,{\mathrm e}^{2}}{5}}{{\mathrm e}-x}\) | \(24\) |
meijerg | \(\frac {34 x}{5 \left (1-{\mathrm e}^{-1} x \right )}+\frac {4 \,{\mathrm e}^{-2} x}{1-{\mathrm e}^{-1} x}-\frac {68 \,{\mathrm e} \left (\frac {x \,{\mathrm e}^{-1}}{1-{\mathrm e}^{-1} x}+\ln \left (1-{\mathrm e}^{-1} x \right )\right )}{5}-\frac {34 \,{\mathrm e} \left (-\frac {x \,{\mathrm e}^{-1} \left (-3 \,{\mathrm e}^{-1} x +6\right )}{3 \left (1-{\mathrm e}^{-1} x \right )}-2 \ln \left (1-{\mathrm e}^{-1} x \right )\right )}{5}\) | \(90\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 14, normalized size = 0.88 \begin {gather*} \frac {34}{5} \, x - \frac {4}{x - e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 14, normalized size = 0.88 \begin {gather*} \frac {34\,x}{5}-\frac {4}{x-\mathrm {e}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 10, normalized size = 0.62 \begin {gather*} \frac {34 x}{5} - \frac {4}{x - e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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