Optimal. Leaf size=22 \[ 5 \left (2-\left (-4+\frac {3}{2 x}+x\right ) \log \left (4 x^2\right )\right ) \]
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Rubi [A]
time = 0.05, antiderivative size = 27, normalized size of antiderivative = 1.23, number of steps
used = 7, number of rules used = 3, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.097, Rules used = {12, 14, 2372}
\begin {gather*} -5 x \log \left (4 x^2\right )-\frac {15 \log \left (4 x^2\right )}{2 x}+40 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2372
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \frac {-30+80 x-20 x^2+\left (15-10 x^2\right ) \log \left (4 x^2\right )}{x^2} \, dx\\ &=\frac {1}{2} \int \left (-\frac {10 \left (3-8 x+2 x^2\right )}{x^2}-\frac {5 \left (-3+2 x^2\right ) \log \left (4 x^2\right )}{x^2}\right ) \, dx\\ &=-\left (\frac {5}{2} \int \frac {\left (-3+2 x^2\right ) \log \left (4 x^2\right )}{x^2} \, dx\right )-5 \int \frac {3-8 x+2 x^2}{x^2} \, dx\\ &=-\frac {5}{2} \left (\frac {3}{x}+2 x\right ) \log \left (4 x^2\right )+5 \int \left (2+\frac {3}{x^2}\right ) \, dx-5 \int \left (2+\frac {3}{x^2}-\frac {8}{x}\right ) \, dx\\ &=40 \log (x)-\frac {5}{2} \left (\frac {3}{x}+2 x\right ) \log \left (4 x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 27, normalized size = 1.23 \begin {gather*} 40 \log (x)-\frac {15 \log \left (4 x^2\right )}{2 x}-5 x \log \left (4 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 34, normalized size = 1.55
method | result | size |
risch | \(-\frac {5 \left (2 x^{2}+3\right ) \ln \left (4 x^{2}\right )}{2 x}+40 \ln \left (x \right )\) | \(24\) |
norman | \(\frac {-5 x^{2} \ln \left (4 x^{2}\right )-\frac {15 \ln \left (4 x^{2}\right )}{2}}{x}+40 \ln \left (x \right )\) | \(30\) |
default | \(40 \ln \left (x \right )-10 x \ln \left (2\right )-\frac {15 \ln \left (2\right )}{x}-5 x \ln \left (x^{2}\right )-\frac {15 \ln \left (x^{2}\right )}{2 x}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 25, normalized size = 1.14 \begin {gather*} -5 \, x \log \left (4 \, x^{2}\right ) - \frac {15 \, \log \left (4 \, x^{2}\right )}{2 \, x} + 40 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 21, normalized size = 0.95 \begin {gather*} -\frac {5 \, {\left (2 \, x^{2} - 8 \, x + 3\right )} \log \left (4 \, x^{2}\right )}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 22, normalized size = 1.00 \begin {gather*} 40 \log {\left (x \right )} + \frac {\left (- 10 x^{2} - 15\right ) \log {\left (4 x^{2} \right )}}{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 22, normalized size = 1.00 \begin {gather*} -\frac {5}{2} \, {\left (2 \, x + \frac {3}{x}\right )} \log \left (4 \, x^{2}\right ) + 40 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.93, size = 21, normalized size = 0.95 \begin {gather*} -\frac {5\,\ln \left (4\,x^2\right )\,\left (2\,x^2-8\,x+3\right )}{2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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