Optimal. Leaf size=48 \[ -\frac {1}{6 x^3}+\frac {13}{8 x^2}-\frac {139}{8 x}-\frac {1417 \log (x)}{16}-\frac {81}{112} \log (2+3 x)+\frac {625}{7} \log (1+5 x) \]
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Rubi [A]
time = 0.03, antiderivative size = 48, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {1368, 723, 814}
\begin {gather*} -\frac {1}{6 x^3}+\frac {13}{8 x^2}-\frac {139}{8 x}-\frac {1417 \log (x)}{16}-\frac {81}{112} \log (3 x+2)+\frac {625}{7} \log (5 x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 723
Rule 814
Rule 1368
Rubi steps
\begin {align*} \int \frac {1}{\left (15+\frac {2}{x^2}+\frac {13}{x}\right ) x^6} \, dx &=\int \frac {1}{x^4 \left (2+13 x+15 x^2\right )} \, dx\\ &=-\frac {1}{6 x^3}+\frac {1}{2} \int \frac {-13-15 x}{x^3 \left (2+13 x+15 x^2\right )} \, dx\\ &=-\frac {1}{6 x^3}+\frac {1}{2} \int \left (-\frac {13}{2 x^3}+\frac {139}{4 x^2}-\frac {1417}{8 x}-\frac {243}{56 (2+3 x)}+\frac {6250}{7 (1+5 x)}\right ) \, dx\\ &=-\frac {1}{6 x^3}+\frac {13}{8 x^2}-\frac {139}{8 x}-\frac {1417 \log (x)}{16}-\frac {81}{112} \log (2+3 x)+\frac {625}{7} \log (1+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 48, normalized size = 1.00 \begin {gather*} -\frac {1}{6 x^3}+\frac {13}{8 x^2}-\frac {139}{8 x}-\frac {1417 \log (x)}{16}-\frac {81}{112} \log (2+3 x)+\frac {625}{7} \log (1+5 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 37, normalized size = 0.77
method | result | size |
risch | \(\frac {-\frac {139}{8} x^{2}+\frac {13}{8} x -\frac {1}{6}}{x^{3}}-\frac {1417 \ln \left (x \right )}{16}-\frac {81 \ln \left (2+3 x \right )}{112}+\frac {625 \ln \left (1+5 x \right )}{7}\) | \(36\) |
default | \(-\frac {1}{6 x^{3}}+\frac {13}{8 x^{2}}-\frac {139}{8 x}-\frac {1417 \ln \left (x \right )}{16}-\frac {81 \ln \left (2+3 x \right )}{112}+\frac {625 \ln \left (1+5 x \right )}{7}\) | \(37\) |
norman | \(\frac {-\frac {1}{6} x^{2}+\frac {13}{8} x^{3}-\frac {139}{8} x^{4}}{x^{5}}-\frac {1417 \ln \left (x \right )}{16}-\frac {81 \ln \left (2+3 x \right )}{112}+\frac {625 \ln \left (1+5 x \right )}{7}\) | \(42\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 36, normalized size = 0.75 \begin {gather*} -\frac {417 \, x^{2} - 39 \, x + 4}{24 \, x^{3}} + \frac {625}{7} \, \log \left (5 \, x + 1\right ) - \frac {81}{112} \, \log \left (3 \, x + 2\right ) - \frac {1417}{16} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 44, normalized size = 0.92 \begin {gather*} \frac {30000 \, x^{3} \log \left (5 \, x + 1\right ) - 243 \, x^{3} \log \left (3 \, x + 2\right ) - 29757 \, x^{3} \log \left (x\right ) - 5838 \, x^{2} + 546 \, x - 56}{336 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 41, normalized size = 0.85 \begin {gather*} - \frac {1417 \log {\left (x \right )}}{16} + \frac {625 \log {\left (x + \frac {1}{5} \right )}}{7} - \frac {81 \log {\left (x + \frac {2}{3} \right )}}{112} + \frac {- 417 x^{2} + 39 x - 4}{24 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.15, size = 39, normalized size = 0.81 \begin {gather*} -\frac {417 \, x^{2} - 39 \, x + 4}{24 \, x^{3}} + \frac {625}{7} \, \log \left ({\left | 5 \, x + 1 \right |}\right ) - \frac {81}{112} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {1417}{16} \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 32, normalized size = 0.67 \begin {gather*} \frac {625\,\ln \left (x+\frac {1}{5}\right )}{7}-\frac {81\,\ln \left (x+\frac {2}{3}\right )}{112}-\frac {1417\,\ln \left (x\right )}{16}-\frac {\frac {139\,x^2}{8}-\frac {13\,x}{8}+\frac {1}{6}}{x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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