Integrand size = 13, antiderivative size = 30 \[ \int x^4 \left (a+b x^4\right )^2 \, dx=\frac {a^2 x^5}{5}+\frac {2}{9} a b x^9+\frac {b^2 x^{13}}{13} \]
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Time = 0.01 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {276} \[ \int x^4 \left (a+b x^4\right )^2 \, dx=\frac {a^2 x^5}{5}+\frac {2}{9} a b x^9+\frac {b^2 x^{13}}{13} \]
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Rule 276
Rubi steps \begin{align*} \text {integral}& = \int \left (a^2 x^4+2 a b x^8+b^2 x^{12}\right ) \, dx \\ & = \frac {a^2 x^5}{5}+\frac {2}{9} a b x^9+\frac {b^2 x^{13}}{13} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int x^4 \left (a+b x^4\right )^2 \, dx=\frac {a^2 x^5}{5}+\frac {2}{9} a b x^9+\frac {b^2 x^{13}}{13} \]
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Time = 3.89 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.83
method | result | size |
gosper | \(\frac {1}{5} x^{5} a^{2}+\frac {2}{9} a b \,x^{9}+\frac {1}{13} b^{2} x^{13}\) | \(25\) |
default | \(\frac {1}{5} x^{5} a^{2}+\frac {2}{9} a b \,x^{9}+\frac {1}{13} b^{2} x^{13}\) | \(25\) |
norman | \(\frac {1}{5} x^{5} a^{2}+\frac {2}{9} a b \,x^{9}+\frac {1}{13} b^{2} x^{13}\) | \(25\) |
risch | \(\frac {1}{5} x^{5} a^{2}+\frac {2}{9} a b \,x^{9}+\frac {1}{13} b^{2} x^{13}\) | \(25\) |
parallelrisch | \(\frac {1}{5} x^{5} a^{2}+\frac {2}{9} a b \,x^{9}+\frac {1}{13} b^{2} x^{13}\) | \(25\) |
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none
Time = 0.25 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.80 \[ \int x^4 \left (a+b x^4\right )^2 \, dx=\frac {1}{13} \, b^{2} x^{13} + \frac {2}{9} \, a b x^{9} + \frac {1}{5} \, a^{2} x^{5} \]
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Time = 0.02 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.87 \[ \int x^4 \left (a+b x^4\right )^2 \, dx=\frac {a^{2} x^{5}}{5} + \frac {2 a b x^{9}}{9} + \frac {b^{2} x^{13}}{13} \]
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none
Time = 0.21 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.80 \[ \int x^4 \left (a+b x^4\right )^2 \, dx=\frac {1}{13} \, b^{2} x^{13} + \frac {2}{9} \, a b x^{9} + \frac {1}{5} \, a^{2} x^{5} \]
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none
Time = 0.26 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.80 \[ \int x^4 \left (a+b x^4\right )^2 \, dx=\frac {1}{13} \, b^{2} x^{13} + \frac {2}{9} \, a b x^{9} + \frac {1}{5} \, a^{2} x^{5} \]
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Time = 0.03 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.80 \[ \int x^4 \left (a+b x^4\right )^2 \, dx=\frac {a^2\,x^5}{5}+\frac {2\,a\,b\,x^9}{9}+\frac {b^2\,x^{13}}{13} \]
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