Optimal. Leaf size=22 \[ \log \left (-25+x-(2+x)^2+\frac {3}{\frac {625}{x^2}+x}\right ) \]
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Rubi [A] time = 0.17, antiderivative size = 33, normalized size of antiderivative = 1.50, number of steps used = 4, number of rules used = 3, integrand size = 66, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {2074, 260, 1587} \begin {gather*} \log \left (x^5+3 x^4+29 x^3+622 x^2+1875 x+18125\right )-\log \left (x^3+625\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 260
Rule 1587
Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {3 x^2}{625+x^3}+\frac {1875+1244 x+87 x^2+12 x^3+5 x^4}{18125+1875 x+622 x^2+29 x^3+3 x^4+x^5}\right ) \, dx\\ &=-\left (3 \int \frac {x^2}{625+x^3} \, dx\right )+\int \frac {1875+1244 x+87 x^2+12 x^3+5 x^4}{18125+1875 x+622 x^2+29 x^3+3 x^4+x^5} \, dx\\ &=-\log \left (625+x^3\right )+\log \left (18125+1875 x+622 x^2+29 x^3+3 x^4+x^5\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 33, normalized size = 1.50 \begin {gather*} -\log \left (625+x^3\right )+\log \left (18125+1875 x+622 x^2+29 x^3+3 x^4+x^5\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.87, size = 33, normalized size = 1.50 \begin {gather*} \log \left (x^{5} + 3 \, x^{4} + 29 \, x^{3} + 622 \, x^{2} + 1875 \, x + 18125\right ) - \log \left (x^{3} + 625\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 35, normalized size = 1.59 \begin {gather*} \log \left ({\left | x^{5} + 3 \, x^{4} + 29 \, x^{3} + 622 \, x^{2} + 1875 \, x + 18125 \right |}\right ) - \log \left ({\left | x^{3} + 625 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 34, normalized size = 1.55
method | result | size |
default | \(\ln \left (x^{5}+3 x^{4}+29 x^{3}+622 x^{2}+1875 x +18125\right )-\ln \left (x^{3}+625\right )\) | \(34\) |
norman | \(\ln \left (x^{5}+3 x^{4}+29 x^{3}+622 x^{2}+1875 x +18125\right )-\ln \left (x^{3}+625\right )\) | \(34\) |
risch | \(\ln \left (x^{5}+3 x^{4}+29 x^{3}+622 x^{2}+1875 x +18125\right )-\ln \left (x^{3}+625\right )\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 33, normalized size = 1.50 \begin {gather*} \log \left (x^{5} + 3 \, x^{4} + 29 \, x^{3} + 622 \, x^{2} + 1875 \, x + 18125\right ) - \log \left (x^{3} + 625\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.19, size = 33, normalized size = 1.50 \begin {gather*} \ln \left (x^5+3\,x^4+29\,x^3+622\,x^2+1875\,x+18125\right )-\ln \left (x^3+625\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 31, normalized size = 1.41 \begin {gather*} - \log {\left (x^{3} + 625 \right )} + \log {\left (x^{5} + 3 x^{4} + 29 x^{3} + 622 x^{2} + 1875 x + 18125 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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