Optimal. Leaf size=20 \[ x+\log \left (-2+3 x-\left (2+\frac {x}{5}\right ) x^3\right ) \]
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Rubi [A] time = 0.07, antiderivative size = 16, normalized size of antiderivative = 0.80, number of steps used = 3, number of rules used = 2, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {6742, 1587} \begin {gather*} \log \left (x^4+10 x^3-15 x+10\right )+x \end {gather*}
Antiderivative was successfully verified.
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Rule 1587
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-\frac {15-30 x^2-4 x^3}{10-15 x+10 x^3+x^4}\right ) \, dx\\ &=x-\int \frac {15-30 x^2-4 x^3}{10-15 x+10 x^3+x^4} \, dx\\ &=x+\log \left (10-15 x+10 x^3+x^4\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 0.80 \begin {gather*} x+\log \left (10-15 x+10 x^3+x^4\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 16, normalized size = 0.80 \begin {gather*} x + \log \left (x^{4} + 10 \, x^{3} - 15 \, x + 10\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 17, normalized size = 0.85 \begin {gather*} x + \log \left ({\left | x^{4} + 10 \, x^{3} - 15 \, x + 10 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 17, normalized size = 0.85
method | result | size |
default | \(x +\ln \left (x^{4}+10 x^{3}-15 x +10\right )\) | \(17\) |
norman | \(x +\ln \left (x^{4}+10 x^{3}-15 x +10\right )\) | \(17\) |
risch | \(x +\ln \left (x^{4}+10 x^{3}-15 x +10\right )\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 16, normalized size = 0.80 \begin {gather*} x + \log \left (x^{4} + 10 \, x^{3} - 15 \, x + 10\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.04, size = 16, normalized size = 0.80 \begin {gather*} x+\ln \left (x^4+10\,x^3-15\,x+10\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 15, normalized size = 0.75 \begin {gather*} x + \log {\left (x^{4} + 10 x^{3} - 15 x + 10 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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