Optimal. Leaf size=25 \[ 4 x \left (16+\log \left (e^{\frac {32}{x \left (\frac {9}{2}-x+x^2\right )}}\right )\right ) \]
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Rubi [A] time = 0.06, antiderivative size = 19, normalized size of antiderivative = 0.76, number of steps used = 5, number of rules used = 5, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.116, Rules used = {1680, 12, 1814, 21, 8} \begin {gather*} 64 x+\frac {512}{4 \left (x-\frac {1}{2}\right )^2+17} \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 12
Rule 21
Rule 1680
Rule 1814
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\operatorname {Subst}\left (\int \frac {64 \left (289-64 x+136 x^2+16 x^4\right )}{\left (17+4 x^2\right )^2} \, dx,x,-\frac {1}{2}+x\right )\\ &=64 \operatorname {Subst}\left (\int \frac {289-64 x+136 x^2+16 x^4}{\left (17+4 x^2\right )^2} \, dx,x,-\frac {1}{2}+x\right )\\ &=\frac {512}{17+(-1+2 x)^2}-\frac {32}{17} \operatorname {Subst}\left (\int \frac {-578-136 x^2}{17+4 x^2} \, dx,x,-\frac {1}{2}+x\right )\\ &=\frac {512}{17+(-1+2 x)^2}+64 \operatorname {Subst}\left (\int 1 \, dx,x,-\frac {1}{2}+x\right )\\ &=64 x+\frac {512}{17+(-1+2 x)^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 0.72 \begin {gather*} 64 \left (x+\frac {4}{9-2 x+2 x^2}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 29, normalized size = 1.16 \begin {gather*} \frac {64 \, {\left (2 \, x^{3} - 2 \, x^{2} + 9 \, x + 4\right )}}{2 \, x^{2} - 2 \, x + 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 18, normalized size = 0.72 \begin {gather*} 64 \, x + \frac {256}{2 \, x^{2} - 2 \, x + 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 17, normalized size = 0.68
method | result | size |
risch | \(64 x +\frac {128}{x^{2}+\frac {9}{2}-x}\) | \(17\) |
default | \(64 x +\frac {256}{2 x^{2}-2 x +9}\) | \(19\) |
norman | \(\frac {128 x^{3}+448 x +832}{2 x^{2}-2 x +9}\) | \(24\) |
gosper | \(\frac {128 x^{3}+448 x +832}{2 x^{2}-2 x +9}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 18, normalized size = 0.72 \begin {gather*} 64 \, x + \frac {256}{2 \, x^{2} - 2 \, x + 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 16, normalized size = 0.64 \begin {gather*} 64\,x+\frac {128}{x^2-x+\frac {9}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 14, normalized size = 0.56 \begin {gather*} 64 x + \frac {256}{2 x^{2} - 2 x + 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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