Optimal. Leaf size=15 \[ \frac {13+e^{3 x/4}}{-4+x} \]
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Rubi [A] time = 0.10, antiderivative size = 26, normalized size of antiderivative = 1.73, number of steps used = 5, number of rules used = 4, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {27, 12, 6742, 2197} \begin {gather*} -\frac {e^{3 x/4}}{4-x}-\frac {13}{4-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 2197
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-52+e^{3 x/4} (-16+3 x)}{4 (-4+x)^2} \, dx\\ &=\frac {1}{4} \int \frac {-52+e^{3 x/4} (-16+3 x)}{(-4+x)^2} \, dx\\ &=\frac {1}{4} \int \left (-\frac {52}{(-4+x)^2}+\frac {e^{3 x/4} (-16+3 x)}{(-4+x)^2}\right ) \, dx\\ &=-\frac {13}{4-x}+\frac {1}{4} \int \frac {e^{3 x/4} (-16+3 x)}{(-4+x)^2} \, dx\\ &=-\frac {13}{4-x}-\frac {e^{3 x/4}}{4-x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 15, normalized size = 1.00 \begin {gather*} \frac {13+e^{3 x/4}}{-4+x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.27, size = 12, normalized size = 0.80 \begin {gather*} \frac {e^{\left (\frac {3}{4} \, x\right )} + 13}{x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 12, normalized size = 0.80 \begin {gather*} \frac {e^{\left (\frac {3}{4} \, x\right )} + 13}{x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.42, size = 13, normalized size = 0.87
method | result | size |
norman | \(\frac {{\mathrm e}^{\frac {3 x}{4}}+13}{x -4}\) | \(13\) |
risch | \(\frac {13}{x -4}+\frac {{\mathrm e}^{\frac {3 x}{4}}}{x -4}\) | \(19\) |
derivativedivides | \(\frac {39}{4 \left (\frac {3 x}{4}-3\right )}+\frac {3 \,{\mathrm e}^{\frac {3 x}{4}}}{4 \left (\frac {3 x}{4}-3\right )}\) | \(24\) |
default | \(\frac {39}{4 \left (\frac {3 x}{4}-3\right )}+\frac {3 \,{\mathrm e}^{\frac {3 x}{4}}}{4 \left (\frac {3 x}{4}-3\right )}\) | \(24\) |
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*} \frac {x e^{\left (\frac {3}{4} \, x\right )}}{x^{2} - 8 \, x + 16} + \frac {4 \, e^{3} E_{2}\left (-\frac {3}{4} \, x + 3\right )}{x - 4} + \frac {13}{x - 4} + \frac {3}{4} \, \int \frac {4 \, {\left (x + 4\right )} e^{\left (\frac {3}{4} \, x\right )}}{3 \, {\left (x^{3} - 12 \, x^{2} + 48 \, x - 64\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 12, normalized size = 0.80 \begin {gather*} \frac {{\mathrm {e}}^{\frac {3\,x}{4}}+13}{x-4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 14, normalized size = 0.93 \begin {gather*} \frac {e^{\frac {3 x}{4}}}{x - 4} + \frac {13}{x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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