Optimal. Leaf size=13 \[ 5-\frac {1}{9 (5+x)}+\log (x) \]
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Rubi [A]
time = 0.02, antiderivative size = 12, normalized size of antiderivative = 0.92, number of steps
used = 5, number of rules used = 4, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.148, Rules used = {1608, 27, 12,
907} \begin {gather*} \log (x)-\frac {1}{9 (x+5)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 907
Rule 1608
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {225+91 x+9 x^2}{x \left (225+90 x+9 x^2\right )} \, dx\\ &=\int \frac {225+91 x+9 x^2}{9 x (5+x)^2} \, dx\\ &=\frac {1}{9} \int \frac {225+91 x+9 x^2}{x (5+x)^2} \, dx\\ &=\frac {1}{9} \int \left (\frac {9}{x}+\frac {1}{(5+x)^2}\right ) \, dx\\ &=-\frac {1}{9 (5+x)}+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 16, normalized size = 1.23 \begin {gather*} \frac {1}{9} \left (-\frac {1}{5+x}+9 \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 11, normalized size = 0.85
method | result | size |
default | \(-\frac {1}{9 \left (5+x \right )}+\ln \left (x \right )\) | \(11\) |
norman | \(-\frac {1}{9 \left (5+x \right )}+\ln \left (x \right )\) | \(11\) |
risch | \(-\frac {1}{9 \left (5+x \right )}+\ln \left (x \right )\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 10, normalized size = 0.77 \begin {gather*} -\frac {1}{9 \, {\left (x + 5\right )}} + \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 = 16, normalized size = 1.23 \begin {gather*} \frac {9 \, {\left (x + 5\right )} \log \left (x\right ) - 1}{9 \, {\left (x + 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 8, normalized size = 0.62 \begin {gather*} \log {\left (x \right )} - \frac {1}{9 x + 45} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 11, normalized size = 0.85 \begin {gather*} -\frac {1}{9 \, {\left (x + 5\right )}} + \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 = 0.04, size = 12, normalized size = 0.92 \begin {gather*} \ln \left (x\right )-\frac {1}{9\,\left (x+5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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