Integrand size = 9, antiderivative size = 17 \[ \int \frac {a+b x}{x^4} \, dx=-\frac {a}{3 x^3}-\frac {b}{2 x^2} \]
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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, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {45} \[ \int \frac {a+b x}{x^4} \, dx=-\frac {a}{3 x^3}-\frac {b}{2 x^2} \]
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Rule 45
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {a}{x^4}+\frac {b}{x^3}\right ) \, dx \\ & = -\frac {a}{3 x^3}-\frac {b}{2 x^2} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \frac {a+b x}{x^4} \, dx=-\frac {a}{3 x^3}-\frac {b}{2 x^2} \]
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Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76
method | result | size |
norman | \(\frac {-\frac {b x}{2}-\frac {a}{3}}{x^{3}}\) | \(13\) |
risch | \(\frac {-\frac {b x}{2}-\frac {a}{3}}{x^{3}}\) | \(13\) |
gosper | \(-\frac {3 b x +2 a}{6 x^{3}}\) | \(14\) |
default | \(-\frac {a}{3 x^{3}}-\frac {b}{2 x^{2}}\) | \(14\) |
parallelrisch | \(\frac {-3 b x -2 a}{6 x^{3}}\) | \(14\) |
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none
Time = 0.22 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \frac {a+b x}{x^4} \, dx=-\frac {3 \, b x + 2 \, a}{6 \, x^{3}} \]
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Time = 0.05 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int \frac {a+b x}{x^4} \, dx=\frac {- 2 a - 3 b x}{6 x^{3}} \]
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none
Time = 0.20 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \frac {a+b x}{x^4} \, dx=-\frac {3 \, b x + 2 \, a}{6 \, x^{3}} \]
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none
Time = 0.28 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \frac {a+b x}{x^4} \, dx=-\frac {3 \, b x + 2 \, a}{6 \, x^{3}} \]
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Time = 0.02 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \frac {a+b x}{x^4} \, dx=-\frac {2\,a+3\,b\,x}{6\,x^3} \]
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