Integrand size = 11, antiderivative size = 13 \[ \int \frac {a+b x^4}{x} \, dx=\frac {b x^4}{4}+a \log (x) \]
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Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14} \[ \int \frac {a+b x^4}{x} \, dx=a \log (x)+\frac {b x^4}{4} \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {a}{x}+b x^3\right ) \, dx \\ & = \frac {b x^4}{4}+a \log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \frac {a+b x^4}{x} \, dx=\frac {b x^4}{4}+a \log (x) \]
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Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92
method | result | size |
default | \(\frac {b \,x^{4}}{4}+a \ln \left (x \right )\) | \(12\) |
norman | \(\frac {b \,x^{4}}{4}+a \ln \left (x \right )\) | \(12\) |
risch | \(\frac {b \,x^{4}}{4}+a \ln \left (x \right )\) | \(12\) |
parallelrisch | \(\frac {b \,x^{4}}{4}+a \ln \left (x \right )\) | \(12\) |
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none
Time = 0.27 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.85 \[ \int \frac {a+b x^4}{x} \, dx=\frac {1}{4} \, b x^{4} + a \log \left (x\right ) \]
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Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \frac {a+b x^4}{x} \, dx=a \log {\left (x \right )} + \frac {b x^{4}}{4} \]
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none
Time = 0.23 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.08 \[ \int \frac {a+b x^4}{x} \, dx=\frac {1}{4} \, b x^{4} + \frac {1}{4} \, a \log \left (x^{4}\right ) \]
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none
Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.08 \[ \int \frac {a+b x^4}{x} \, dx=\frac {1}{4} \, b x^{4} + \frac {1}{4} \, a \log \left (x^{4}\right ) \]
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Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.85 \[ \int \frac {a+b x^4}{x} \, dx=\frac {b\,x^4}{4}+a\,\ln \left (x\right ) \]
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