Integrand size = 15, antiderivative size = 18 \[ \int \frac {-4+4 x^5-\log (x)}{x^2} \, dx=\frac {5-2 x+x \left (6+x^4\right )+\log (x)}{x} \]
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Time = 0.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83, number of steps used = 5, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {14, 2341} \[ \int \frac {-4+4 x^5-\log (x)}{x^2} \, dx=x^4+\frac {5}{x}+\frac {\log (x)}{x} \]
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Rule 14
Rule 2341
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {4 \left (-1+x^5\right )}{x^2}-\frac {\log (x)}{x^2}\right ) \, dx \\ & = 4 \int \frac {-1+x^5}{x^2} \, dx-\int \frac {\log (x)}{x^2} \, dx \\ & = \frac {1}{x}+\frac {\log (x)}{x}+4 \int \left (-\frac {1}{x^2}+x^3\right ) \, dx \\ & = \frac {5}{x}+x^4+\frac {\log (x)}{x} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \frac {-4+4 x^5-\log (x)}{x^2} \, dx=\frac {5}{x}+x^4+\frac {\log (x)}{x} \]
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Time = 0.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.67
method | result | size |
norman | \(\frac {5+x^{5}+\ln \left (x \right )}{x}\) | \(12\) |
parallelrisch | \(\frac {5+x^{5}+\ln \left (x \right )}{x}\) | \(12\) |
default | \(x^{4}+\frac {\ln \left (x \right )}{x}+\frac {5}{x}\) | \(16\) |
parts | \(x^{4}+\frac {\ln \left (x \right )}{x}+\frac {5}{x}\) | \(16\) |
risch | \(\frac {\ln \left (x \right )}{x}+\frac {x^{5}+5}{x}\) | \(17\) |
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Time = 0.25 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.61 \[ \int \frac {-4+4 x^5-\log (x)}{x^2} \, dx=\frac {x^{5} + \log \left (x\right ) + 5}{x} \]
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Time = 0.06 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.56 \[ \int \frac {-4+4 x^5-\log (x)}{x^2} \, dx=x^{4} + \frac {\log {\left (x \right )}}{x} + \frac {5}{x} \]
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Time = 0.19 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \frac {-4+4 x^5-\log (x)}{x^2} \, dx=x^{4} + \frac {\log \left (x\right )}{x} + \frac {5}{x} \]
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Time = 0.26 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \frac {-4+4 x^5-\log (x)}{x^2} \, dx=x^{4} + \frac {\log \left (x\right )}{x} + \frac {5}{x} \]
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Time = 9.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.67 \[ \int \frac {-4+4 x^5-\log (x)}{x^2} \, dx=\frac {\ln \left (x\right )+5}{x}+x^4 \]
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