Optimal. Leaf size=49 \[ \frac{1003 \log \left (x^2-10 x+26\right )}{1025}+\frac{22 \log \left (x^2-2 x+17\right )}{1025}-\frac{15033 \tan ^{-1}(5-x)}{1025}-\frac{4607 \tan ^{-1}\left (\frac{x-1}{4}\right )}{4100} \]
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Rubi [A] time = 0.156707, antiderivative size = 49, normalized size of antiderivative = 1., number of steps used = 10, number of rules used = 5, integrand size = 36, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.139, Rules used = {6728, 634, 618, 204, 628} \[ \frac{1003 \log \left (x^2-10 x+26\right )}{1025}+\frac{22 \log \left (x^2-2 x+17\right )}{1025}-\frac{15033 \tan ^{-1}(5-x)}{1025}-\frac{4607 \tan ^{-1}\left (\frac{x-1}{4}\right )}{4100} \]
Antiderivative was successfully verified.
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Rule 6728
Rule 634
Rule 618
Rule 204
Rule 628
Rubi steps
\begin{align*} \int \frac{-35+70 x-4 x^2+2 x^3}{\left (26-10 x+x^2\right ) \left (17-2 x+x^2\right )} \, dx &=\int \left (\frac{5003+2006 x}{1025 \left (26-10 x+x^2\right )}+\frac{-4651+44 x}{1025 \left (17-2 x+x^2\right )}\right ) \, dx\\ &=\frac{\int \frac{5003+2006 x}{26-10 x+x^2} \, dx}{1025}+\frac{\int \frac{-4651+44 x}{17-2 x+x^2} \, dx}{1025}\\ &=\frac{22 \int \frac{-2+2 x}{17-2 x+x^2} \, dx}{1025}+\frac{1003 \int \frac{-10+2 x}{26-10 x+x^2} \, dx}{1025}-\frac{4607 \int \frac{1}{17-2 x+x^2} \, dx}{1025}+\frac{15033 \int \frac{1}{26-10 x+x^2} \, dx}{1025}\\ &=\frac{1003 \log \left (26-10 x+x^2\right )}{1025}+\frac{22 \log \left (17-2 x+x^2\right )}{1025}+\frac{9214 \operatorname{Subst}\left (\int \frac{1}{-64-x^2} \, dx,x,-2+2 x\right )}{1025}-\frac{30066 \operatorname{Subst}\left (\int \frac{1}{-4-x^2} \, dx,x,-10+2 x\right )}{1025}\\ &=-\frac{15033 \tan ^{-1}(5-x)}{1025}-\frac{4607 \tan ^{-1}\left (\frac{1}{4} (-1+x)\right )}{4100}+\frac{1003 \log \left (26-10 x+x^2\right )}{1025}+\frac{22 \log \left (17-2 x+x^2\right )}{1025}\\ \end{align*}
Mathematica [A] time = 0.0135432, size = 49, normalized size = 1. \[ \frac{1003 \log \left (x^2-10 x+26\right )}{1025}+\frac{22 \log \left (x^2-2 x+17\right )}{1025}-\frac{15033 \tan ^{-1}(5-x)}{1025}-\frac{4607 \tan ^{-1}\left (\frac{x-1}{4}\right )}{4100} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 38, normalized size = 0.8 \begin{align*}{\frac{15033\,\arctan \left ( -5+x \right ) }{1025}}-{\frac{4607}{4100}\arctan \left ({\frac{x}{4}}-{\frac{1}{4}} \right ) }+{\frac{1003\,\ln \left ({x}^{2}-10\,x+26 \right ) }{1025}}+{\frac{22\,\ln \left ({x}^{2}-2\,x+17 \right ) }{1025}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.4725, size = 50, normalized size = 1.02 \begin{align*} \frac{15033}{1025} \, \arctan \left (x - 5\right ) - \frac{4607}{4100} \, \arctan \left (\frac{1}{4} \, x - \frac{1}{4}\right ) + \frac{22}{1025} \, \log \left (x^{2} - 2 \, x + 17\right ) + \frac{1003}{1025} \, \log \left (x^{2} - 10 \, x + 26\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.67226, size = 163, normalized size = 3.33 \begin{align*} \frac{15033}{1025} \, \arctan \left (x - 5\right ) - \frac{4607}{4100} \, \arctan \left (\frac{1}{4} \, x - \frac{1}{4}\right ) + \frac{22}{1025} \, \log \left (x^{2} - 2 \, x + 17\right ) + \frac{1003}{1025} \, \log \left (x^{2} - 10 \, x + 26\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.195851, size = 46, normalized size = 0.94 \begin{align*} \frac{1003 \log{\left (x^{2} - 10 x + 26 \right )}}{1025} + \frac{22 \log{\left (x^{2} - 2 x + 17 \right )}}{1025} - \frac{4607 \operatorname{atan}{\left (\frac{x}{4} - \frac{1}{4} \right )}}{4100} + \frac{15033 \operatorname{atan}{\left (x - 5 \right )}}{1025} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12058, size = 50, normalized size = 1.02 \begin{align*} \frac{15033}{1025} \, \arctan \left (x - 5\right ) - \frac{4607}{4100} \, \arctan \left (\frac{1}{4} \, x - \frac{1}{4}\right ) + \frac{22}{1025} \, \log \left (x^{2} - 2 \, x + 17\right ) + \frac{1003}{1025} \, \log \left (x^{2} - 10 \, x + 26\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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