Integrand size = 15, antiderivative size = 17 \[ \int \frac {b x^2+c x^4}{x^7} \, dx=-\frac {b}{4 x^4}-\frac {c}{2 x^2} \]
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Time = 0.00 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {14} \[ \int \frac {b x^2+c x^4}{x^7} \, dx=-\frac {b}{4 x^4}-\frac {c}{2 x^2} \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {b}{x^5}+\frac {c}{x^3}\right ) \, dx \\ & = -\frac {b}{4 x^4}-\frac {c}{2 x^2} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \frac {b x^2+c x^4}{x^7} \, dx=-\frac {b}{4 x^4}-\frac {c}{2 x^2} \]
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Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82
method | result | size |
gosper | \(-\frac {2 c \,x^{2}+b}{4 x^{4}}\) | \(14\) |
default | \(-\frac {b}{4 x^{4}}-\frac {c}{2 x^{2}}\) | \(14\) |
risch | \(\frac {-\frac {c \,x^{2}}{2}-\frac {b}{4}}{x^{4}}\) | \(15\) |
parallelrisch | \(\frac {-2 c \,x^{2}-b}{4 x^{4}}\) | \(16\) |
norman | \(\frac {-\frac {1}{4} b \,x^{2}-\frac {1}{2} c \,x^{4}}{x^{6}}\) | \(18\) |
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none
Time = 0.25 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \frac {b x^2+c x^4}{x^7} \, dx=-\frac {2 \, c x^{2} + b}{4 \, x^{4}} \]
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Time = 0.06 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int \frac {b x^2+c x^4}{x^7} \, dx=\frac {- b - 2 c x^{2}}{4 x^{4}} \]
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none
Time = 0.19 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \frac {b x^2+c x^4}{x^7} \, dx=-\frac {2 \, c x^{2} + b}{4 \, x^{4}} \]
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none
Time = 0.29 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \frac {b x^2+c x^4}{x^7} \, dx=-\frac {2 \, c x^{2} + b}{4 \, x^{4}} \]
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Time = 0.03 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \frac {b x^2+c x^4}{x^7} \, dx=-\frac {2\,c\,x^2+b}{4\,x^4} \]
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