Optimal. Leaf size=16 \[ \frac {x \log \left ((1-5 x)^2 x\right )}{\log (2)} \]
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Rubi [A]
time = 0.08, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps
used = 8, number of rules used = 6, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 6874, 45,
2579, 31, 8} \begin {gather*} \frac {x \log \left ((1-5 x)^2 x\right )}{\log (2)} \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 12
Rule 31
Rule 45
Rule 2579
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-1+15 x+(-1+5 x) \log \left (x-10 x^2+25 x^3\right )}{-1+5 x} \, dx}{\log (2)}\\ &=\frac {\int \left (\frac {-1+15 x}{-1+5 x}+\log \left (x (-1+5 x)^2\right )\right ) \, dx}{\log (2)}\\ &=\frac {\int \frac {-1+15 x}{-1+5 x} \, dx}{\log (2)}+\frac {\int \log \left (x (-1+5 x)^2\right ) \, dx}{\log (2)}\\ &=\frac {x \log \left ((1-5 x)^2 x\right )}{\log (2)}+\frac {\int \left (3+\frac {2}{-1+5 x}\right ) \, dx}{\log (2)}-\frac {2 \int \frac {1}{-1+5 x} \, dx}{\log (2)}-\frac {3 \int 1 \, dx}{\log (2)}\\ &=\frac {x \log \left ((1-5 x)^2 x\right )}{\log (2)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 16, normalized size = 1.00 \begin {gather*} \frac {x \log \left (x (-1+5 x)^2\right )}{\log (2)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.65, size = 20, normalized size = 1.25
method | result | size |
default | \(\frac {\ln \left (25 x^{3}-10 x^{2}+x \right ) x}{\ln \left (2\right )}\) | \(20\) |
norman | \(\frac {\ln \left (25 x^{3}-10 x^{2}+x \right ) x}{\ln \left (2\right )}\) | \(20\) |
risch | \(\frac {\ln \left (25 x^{3}-10 x^{2}+x \right ) x}{\ln \left (2\right )}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 33 vs.
\(2 (16) = 32\).
time = 0.30, size = 33, normalized size = 2.06 \begin {gather*} \frac {2 \, {\left (5 \, x - 1\right )} \log \left (5 \, x - 1\right ) + 5 \, x \log \left (x\right ) + 2 \, \log \left (5 \, x - 1\right )}{5 \, \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 19, normalized size = 1.19 \begin {gather*} \frac {x \log \left (25 \, x^{3} - 10 \, x^{2} + x\right )}{\log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 17, normalized size = 1.06 \begin {gather*} \frac {x \log {\left (25 x^{3} - 10 x^{2} + x \right )}}{\log {\left (2 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 19, normalized size = 1.19 \begin {gather*} \frac {x \log \left (25 \, x^{3} - 10 \, x^{2} + x\right )}{\log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.21, size = 16, normalized size = 1.00 \begin {gather*} \frac {x\,\ln \left (x\,{\left (5\,x-1\right )}^2\right )}{\ln \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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