Integrand size = 11, antiderivative size = 15 \[ \int \frac {a+b x^3}{x^5} \, dx=-\frac {a}{4 x^4}-\frac {b}{x} \]
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Time = 0.00 (sec) , antiderivative size = 15, 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} \[ \int \frac {a+b x^3}{x^5} \, dx=-\frac {a}{4 x^4}-\frac {b}{x} \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {a}{x^5}+\frac {b}{x^2}\right ) \, dx \\ & = -\frac {a}{4 x^4}-\frac {b}{x} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \frac {a+b x^3}{x^5} \, dx=-\frac {a}{4 x^4}-\frac {b}{x} \]
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Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93
method | result | size |
gosper | \(-\frac {4 b \,x^{3}+a}{4 x^{4}}\) | \(14\) |
default | \(-\frac {a}{4 x^{4}}-\frac {b}{x}\) | \(14\) |
norman | \(\frac {-b \,x^{3}-\frac {a}{4}}{x^{4}}\) | \(15\) |
risch | \(\frac {-b \,x^{3}-\frac {a}{4}}{x^{4}}\) | \(15\) |
parallelrisch | \(\frac {-4 b \,x^{3}-a}{4 x^{4}}\) | \(16\) |
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none
Time = 0.23 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int \frac {a+b x^3}{x^5} \, dx=-\frac {4 \, b x^{3} + a}{4 \, x^{4}} \]
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Time = 0.05 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {a+b x^3}{x^5} \, dx=\frac {- a - 4 b x^{3}}{4 x^{4}} \]
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none
Time = 0.19 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int \frac {a+b x^3}{x^5} \, dx=-\frac {4 \, b x^{3} + a}{4 \, x^{4}} \]
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none
Time = 0.36 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int \frac {a+b x^3}{x^5} \, dx=-\frac {4 \, b x^{3} + a}{4 \, x^{4}} \]
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Time = 0.02 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int \frac {a+b x^3}{x^5} \, dx=-\frac {4\,b\,x^3+a}{4\,x^4} \]
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