Integrand size = 7, antiderivative size = 12 \[ \int \left (a+b x^4\right ) \, dx=a x+\frac {b x^5}{5} \]
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Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (a+b x^4\right ) \, dx=a x+\frac {b x^5}{5} \]
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Rubi steps \begin{align*} \text {integral}& = a x+\frac {b x^5}{5} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \left (a+b x^4\right ) \, dx=a x+\frac {b x^5}{5} \]
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Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92
method | result | size |
gosper | \(a x +\frac {1}{5} b \,x^{5}\) | \(11\) |
default | \(a x +\frac {1}{5} b \,x^{5}\) | \(11\) |
norman | \(a x +\frac {1}{5} b \,x^{5}\) | \(11\) |
risch | \(a x +\frac {1}{5} b \,x^{5}\) | \(11\) |
parallelrisch | \(a x +\frac {1}{5} b \,x^{5}\) | \(11\) |
parts | \(a x +\frac {1}{5} b \,x^{5}\) | \(11\) |
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none
Time = 0.25 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (a+b x^4\right ) \, dx=\frac {1}{5} \, b x^{5} + a x \]
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Time = 0.01 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \left (a+b x^4\right ) \, dx=a x + \frac {b x^{5}}{5} \]
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none
Time = 0.20 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (a+b x^4\right ) \, dx=\frac {1}{5} \, b x^{5} + a x \]
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none
Time = 0.27 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (a+b x^4\right ) \, dx=\frac {1}{5} \, b x^{5} + a x \]
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Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (a+b x^4\right ) \, dx=\frac {b\,x^5}{5}+a\,x \]
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