Optimal. Leaf size=33 \[ \frac {x^2}{30}-\frac {13 x}{225}+\frac {8}{189} \log (3 x+2)-\frac {1}{875} \log (5 x+1) \]
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Rubi [A] time = 0.02, antiderivative size = 33, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 4, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {1386, 701, 632, 31} \begin {gather*} \frac {x^2}{30}-\frac {13 x}{225}+\frac {8}{189} \log (3 x+2)-\frac {1}{875} \log (5 x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rule 632
Rule 701
Rule 1386
Rubi steps
\begin {align*} \int \frac {x^2}{13+\frac {2}{x}+15 x} \, dx &=\int \frac {x^3}{2+13 x+15 x^2} \, dx\\ &=\int \left (-\frac {13}{225}+\frac {x}{15}+\frac {26+139 x}{225 \left (2+13 x+15 x^2\right )}\right ) \, dx\\ &=-\frac {13 x}{225}+\frac {x^2}{30}+\frac {1}{225} \int \frac {26+139 x}{2+13 x+15 x^2} \, dx\\ &=-\frac {13 x}{225}+\frac {x^2}{30}-\frac {3}{175} \int \frac {1}{3+15 x} \, dx+\frac {40}{63} \int \frac {1}{10+15 x} \, dx\\ &=-\frac {13 x}{225}+\frac {x^2}{30}+\frac {8}{189} \log (2+3 x)-\frac {1}{875} \log (1+5 x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 33, normalized size = 1.00 \begin {gather*} \frac {x^2}{30}-\frac {13 x}{225}+\frac {8}{189} \log (3 x+2)-\frac {1}{875} \log (5 x+1) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^2}{13+\frac {2}{x}+15 x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.93, size = 25, normalized size = 0.76 \begin {gather*} \frac {1}{30} \, x^{2} - \frac {13}{225} \, x - \frac {1}{875} \, \log \left (5 \, x + 1\right ) + \frac {8}{189} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.34, size = 27, normalized size = 0.82 \begin {gather*} \frac {1}{30} \, x^{2} - \frac {13}{225} \, x - \frac {1}{875} \, \log \left ({\left | 5 \, x + 1 \right |}\right ) + \frac {8}{189} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 26, normalized size = 0.79 \begin {gather*} \frac {x^{2}}{30}-\frac {13 x}{225}-\frac {\ln \left (5 x +1\right )}{875}+\frac {8 \ln \left (3 x +2\right )}{189} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.02, size = 25, normalized size = 0.76 \begin {gather*} \frac {1}{30} \, x^{2} - \frac {13}{225} \, x - \frac {1}{875} \, \log \left (5 \, x + 1\right ) + \frac {8}{189} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 21, normalized size = 0.64 \begin {gather*} \frac {8\,\ln \left (x+\frac {2}{3}\right )}{189}-\frac {13\,x}{225}-\frac {\ln \left (x+\frac {1}{5}\right )}{875}+\frac {x^2}{30} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 27, normalized size = 0.82 \begin {gather*} \frac {x^{2}}{30} - \frac {13 x}{225} - \frac {\log {\left (x + \frac {1}{5} \right )}}{875} + \frac {8 \log {\left (x + \frac {2}{3} \right )}}{189} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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