Integrand size = 16, antiderivative size = 25 \[ \int \frac {a+b x^2+c x^4}{x^7} \, dx=-\frac {a}{6 x^6}-\frac {b}{4 x^4}-\frac {c}{2 x^2} \]
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Time = 0.00 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {14} \[ \int \frac {a+b x^2+c x^4}{x^7} \, dx=-\frac {a}{6 x^6}-\frac {b}{4 x^4}-\frac {c}{2 x^2} \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {a}{x^7}+\frac {b}{x^5}+\frac {c}{x^3}\right ) \, dx \\ & = -\frac {a}{6 x^6}-\frac {b}{4 x^4}-\frac {c}{2 x^2} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00 \[ \int \frac {a+b x^2+c x^4}{x^7} \, dx=-\frac {a}{6 x^6}-\frac {b}{4 x^4}-\frac {c}{2 x^2} \]
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Time = 0.02 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.80
method | result | size |
default | \(-\frac {a}{6 x^{6}}-\frac {b}{4 x^{4}}-\frac {c}{2 x^{2}}\) | \(20\) |
norman | \(\frac {-\frac {1}{2} c \,x^{4}-\frac {1}{4} b \,x^{2}-\frac {1}{6} a}{x^{6}}\) | \(21\) |
risch | \(\frac {-\frac {1}{2} c \,x^{4}-\frac {1}{4} b \,x^{2}-\frac {1}{6} a}{x^{6}}\) | \(21\) |
gosper | \(-\frac {6 c \,x^{4}+3 b \,x^{2}+2 a}{12 x^{6}}\) | \(22\) |
parallelrisch | \(\frac {-6 c \,x^{4}-3 b \,x^{2}-2 a}{12 x^{6}}\) | \(22\) |
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Time = 0.23 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.84 \[ \int \frac {a+b x^2+c x^4}{x^7} \, dx=-\frac {6 \, c x^{4} + 3 \, b x^{2} + 2 \, a}{12 \, x^{6}} \]
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Time = 0.16 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.88 \[ \int \frac {a+b x^2+c x^4}{x^7} \, dx=\frac {- 2 a - 3 b x^{2} - 6 c x^{4}}{12 x^{6}} \]
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Time = 0.20 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.84 \[ \int \frac {a+b x^2+c x^4}{x^7} \, dx=-\frac {6 \, c x^{4} + 3 \, b x^{2} + 2 \, a}{12 \, x^{6}} \]
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Time = 0.30 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.84 \[ \int \frac {a+b x^2+c x^4}{x^7} \, dx=-\frac {6 \, c x^{4} + 3 \, b x^{2} + 2 \, a}{12 \, x^{6}} \]
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Time = 0.03 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.84 \[ \int \frac {a+b x^2+c x^4}{x^7} \, dx=-\frac {\frac {c\,x^4}{2}+\frac {b\,x^2}{4}+\frac {a}{6}}{x^6} \]
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