Integrand size = 11, antiderivative size = 17 \[ \int \left (a+\frac {b}{x^2}\right ) x^6 \, dx=\frac {b x^5}{5}+\frac {a x^7}{7} \]
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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, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14} \[ \int \left (a+\frac {b}{x^2}\right ) x^6 \, dx=\frac {a x^7}{7}+\frac {b x^5}{5} \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (b x^4+a x^6\right ) \, dx \\ & = \frac {b x^5}{5}+\frac {a x^7}{7} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \left (a+\frac {b}{x^2}\right ) x^6 \, dx=\frac {b x^5}{5}+\frac {a x^7}{7} \]
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Time = 0.05 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82
method | result | size |
default | \(\frac {1}{5} b \,x^{5}+\frac {1}{7} a \,x^{7}\) | \(14\) |
risch | \(\frac {1}{5} b \,x^{5}+\frac {1}{7} a \,x^{7}\) | \(14\) |
parallelrisch | \(\frac {1}{5} b \,x^{5}+\frac {1}{7} a \,x^{7}\) | \(14\) |
gosper | \(\frac {x^{5} \left (5 a \,x^{2}+7 b \right )}{35}\) | \(16\) |
norman | \(\frac {\frac {1}{7} a \,x^{8}+\frac {1}{5} b \,x^{6}}{x}\) | \(18\) |
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none
Time = 0.23 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \left (a+\frac {b}{x^2}\right ) x^6 \, dx=\frac {1}{7} \, a x^{7} + \frac {1}{5} \, b x^{5} \]
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Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.71 \[ \int \left (a+\frac {b}{x^2}\right ) x^6 \, dx=\frac {a x^{7}}{7} + \frac {b x^{5}}{5} \]
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none
Time = 0.19 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \left (a+\frac {b}{x^2}\right ) x^6 \, dx=\frac {1}{7} \, a x^{7} + \frac {1}{5} \, b x^{5} \]
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none
Time = 0.27 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \left (a+\frac {b}{x^2}\right ) x^6 \, dx=\frac {1}{7} \, a x^{7} + \frac {1}{5} \, b x^{5} \]
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Time = 0.03 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \left (a+\frac {b}{x^2}\right ) x^6 \, dx=\frac {a\,x^7}{7}+\frac {b\,x^5}{5} \]
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