Optimal. Leaf size=18 \[ -\frac {1}{3 x^3}-\frac {1}{x^2}-\frac {1}{x} \]
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Rubi [A]
time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {14}
\begin {gather*} -\frac {1}{3 x^3}-\frac {1}{x^2}-\frac {1}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {1+2 x+x^2}{x^4} \, dx &=\int \left (\frac {1}{x^4}+\frac {2}{x^3}+\frac {1}{x^2}\right ) \, dx\\ &=-\frac {1}{3 x^3}-\frac {1}{x^2}-\frac {1}{x}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 18, normalized size = 1.00 \begin {gather*} -\frac {1}{3 x^3}-\frac {1}{x^2}-\frac {1}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 17, normalized size = 0.94
method | result | size |
norman | \(\frac {-x^{2}-x -\frac {1}{3}}{x^{3}}\) | \(15\) |
risch | \(\frac {-x^{2}-x -\frac {1}{3}}{x^{3}}\) | \(15\) |
gosper | \(-\frac {3 x^{2}+3 x +1}{3 x^{3}}\) | \(16\) |
default | \(-\frac {1}{3 x^{3}}-\frac {1}{x^{2}}-\frac {1}{x}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 15, normalized size = 0.83 \begin {gather*} -\frac {3 \, x^{2} + 3 \, x + 1}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.09, size = 15, normalized size = 0.83 \begin {gather*} -\frac {3 \, x^{2} + 3 \, x + 1}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 15, normalized size = 0.83 \begin {gather*} \frac {- 3 x^{2} - 3 x - 1}{3 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.74, size = 15, normalized size = 0.83 \begin {gather*} -\frac {3 \, x^{2} + 3 \, x + 1}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 11, normalized size = 0.61 \begin {gather*} -\frac {x^2+x+\frac {1}{3}}{x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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