Integrand size = 8, antiderivative size = 12 \[ \int \frac {400+\log (18)}{x^2} \, dx=5+e-\frac {400+\log (18)}{x} \]
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Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 30} \[ \int \frac {400+\log (18)}{x^2} \, dx=-\frac {400+\log (18)}{x} \]
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Rule 12
Rule 30
Rubi steps \begin{align*} \text {integral}& = (400+\log (18)) \int \frac {1}{x^2} \, dx \\ & = -\frac {400+\log (18)}{x} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int \frac {400+\log (18)}{x^2} \, dx=-\frac {400+\log (18)}{x} \]
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Time = 0.06 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83
method | result | size |
gosper | \(-\frac {\ln \left (18\right )+400}{x}\) | \(10\) |
default | \(-\frac {\ln \left (18\right )+400}{x}\) | \(10\) |
parallelrisch | \(-\frac {\ln \left (18\right )+400}{x}\) | \(10\) |
norman | \(\frac {-\ln \left (18\right )-400}{x}\) | \(11\) |
risch | \(-\frac {\ln \left (2\right )}{x}-\frac {2 \ln \left (3\right )}{x}-\frac {400}{x}\) | \(21\) |
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none
Time = 0.23 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int \frac {400+\log (18)}{x^2} \, dx=-\frac {\log \left (18\right ) + 400}{x} \]
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Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.58 \[ \int \frac {400+\log (18)}{x^2} \, dx=- \frac {\log {\left (18 \right )} + 400}{x} \]
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none
Time = 0.17 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int \frac {400+\log (18)}{x^2} \, dx=-\frac {\log \left (18\right ) + 400}{x} \]
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none
Time = 0.26 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int \frac {400+\log (18)}{x^2} \, dx=-\frac {\log \left (18\right ) + 400}{x} \]
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Time = 0.03 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int \frac {400+\log (18)}{x^2} \, dx=-\frac {\ln \left (18\right )+400}{x} \]
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