Optimal. Leaf size=31 \[ 3 e^{-x} \left (\frac {8}{4-\frac {3 (1-x)}{4}}-e^x (3+x)\right ) \]
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Rubi [A]
time = 0.16, antiderivative size = 18, normalized size of antiderivative = 0.58, number of steps
used = 4, number of rules used = 3, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.081, Rules used = {27, 6874, 2228}
\begin {gather*} \frac {96 e^{-x}}{3 x+13}-3 x \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 2228
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-x} \left (-1536-288 x+e^x \left (-507-234 x-27 x^2\right )\right )}{(13+3 x)^2} \, dx\\ &=\int \left (-3-\frac {96 e^{-x} (16+3 x)}{(13+3 x)^2}\right ) \, dx\\ &=-3 x-96 \int \frac {e^{-x} (16+3 x)}{(13+3 x)^2} \, dx\\ &=-3 x+\frac {96 e^{-x}}{13+3 x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.90, size = 24, normalized size = 0.77 \begin {gather*} -\frac {3 \left (-96 e^{-x}+(13+3 x)^2\right )}{39+9 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.69, size = 18, normalized size = 0.58
method | result | size |
default | \(-3 x +\frac {96 \,{\mathrm e}^{-x}}{3 x +13}\) | \(18\) |
risch | \(-3 x +\frac {96 \,{\mathrm e}^{-x}}{3 x +13}\) | \(18\) |
norman | \(\frac {\left (96+169 \,{\mathrm e}^{x}-9 \,{\mathrm e}^{x} x^{2}\right ) {\mathrm e}^{-x}}{3 x +13}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 27, normalized size = 0.87 \begin {gather*} -\frac {3 \, {\left ({\left (3 \, x^{2} + 13 \, x\right )} e^{x} - 32\right )} e^{\left (-x\right )}}{3 \, x + 13} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 12, normalized size = 0.39 \begin {gather*} - 3 x + \frac {96 e^{- x}}{3 x + 13} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 24, normalized size = 0.77 \begin {gather*} -\frac {3 \, {\left (3 \, x^{2} + 13 \, x - 32 \, e^{\left (-x\right )}\right )}}{3 \, x + 13} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.11, size = 18, normalized size = 0.58 \begin {gather*} \frac {96}{13\,{\mathrm {e}}^x+3\,x\,{\mathrm {e}}^x}-3\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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