Optimal. Leaf size=17 \[ 1-\frac {e^{-1+x}}{x}+x+\log (676+x) \]
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Rubi [A] time = 0.33, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps used = 6, number of rules used = 4, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.108, Rules used = {1593, 6742, 2197, 43} \begin {gather*} x-\frac {e^{x-1}}{x}+\log (x+676) \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 1593
Rule 2197
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {677 x^2+x^3+e^{-1+x} \left (676-675 x-x^2\right )}{x^2 (676+x)} \, dx\\ &=\int \left (-\frac {e^{-1+x} (-1+x)}{x^2}+\frac {677+x}{676+x}\right ) \, dx\\ &=-\int \frac {e^{-1+x} (-1+x)}{x^2} \, dx+\int \frac {677+x}{676+x} \, dx\\ &=-\frac {e^{-1+x}}{x}+\int \left (1+\frac {1}{676+x}\right ) \, dx\\ &=-\frac {e^{-1+x}}{x}+x+\log (676+x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 22, normalized size = 1.29 \begin {gather*} \frac {-\frac {e^x}{x}+e x+e \log (676+x)}{e} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 20, normalized size = 1.18 \begin {gather*} \frac {x^{2} + x \log \left (x + 676\right ) - e^{\left (x - 1\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 25, normalized size = 1.47 \begin {gather*} \frac {{\left (x^{2} e + x e \log \left (x + 676\right ) - e^{x}\right )} e^{\left (-1\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 16, normalized size = 0.94
method | result | size |
risch | \(x +\ln \left (676+x \right )-\frac {{\mathrm e}^{x -1}}{x}\) | \(16\) |
derivativedivides | \(x -1+\ln \left (676+x \right )-\frac {{\mathrm e}^{x -1}}{x}\) | \(17\) |
default | \(x -1+\ln \left (676+x \right )-\frac {{\mathrm e}^{x -1}}{x}\) | \(17\) |
norman | \(\frac {x^{2}-{\mathrm e}^{x -1}}{x}+\ln \left (676+x \right )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 15, normalized size = 0.88 \begin {gather*} x - \frac {e^{\left (x - 1\right )}}{x} + \log \left (x + 676\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.14, size = 20, normalized size = 1.18 \begin {gather*} \ln \left (x+676\right )-\frac {{\mathrm {e}}^{x-1}-x^2}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 12, normalized size = 0.71 \begin {gather*} x + \log {\left (x + 676 \right )} - \frac {e^{x - 1}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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