Integrand size = 24, antiderivative size = 55 \[ \int \frac {x}{\sqrt {-17+18 x-11 x^2+6 x^3+x^4}} \, dx=-\frac {1}{4} \log \left (-11-68 x^2-24 x^3-2 x^4+\left (34+18 x+2 x^2\right ) \sqrt {-17+18 x-11 x^2+6 x^3+x^4}\right ) \]
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\[ \int \frac {x}{\sqrt {-17+18 x-11 x^2+6 x^3+x^4}} \, dx=\int \frac {x}{\sqrt {-17+18 x-11 x^2+6 x^3+x^4}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {x}{\sqrt {-17+18 x-11 x^2+6 x^3+x^4}} \, dx \\ \end{align*}
Time = 3.84 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.00 \[ \int \frac {x}{\sqrt {-17+18 x-11 x^2+6 x^3+x^4}} \, dx=-\frac {1}{4} \log \left (-11-68 x^2-24 x^3-2 x^4+\left (34+18 x+2 x^2\right ) \sqrt {-17+18 x-11 x^2+6 x^3+x^4}\right ) \]
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Time = 1.50 (sec) , antiderivative size = 91, normalized size of antiderivative = 1.65
method | result | size |
default | \(\frac {\ln \left (2 x^{4}+2 \sqrt {x^{4}+6 x^{3}-11 x^{2}+18 x -17}\, x^{2}+24 x^{3}+18 x \sqrt {x^{4}+6 x^{3}-11 x^{2}+18 x -17}+68 x^{2}+34 \sqrt {x^{4}+6 x^{3}-11 x^{2}+18 x -17}+11\right )}{4}\) | \(91\) |
trager | \(\frac {\ln \left (2 x^{4}+2 \sqrt {x^{4}+6 x^{3}-11 x^{2}+18 x -17}\, x^{2}+24 x^{3}+18 x \sqrt {x^{4}+6 x^{3}-11 x^{2}+18 x -17}+68 x^{2}+34 \sqrt {x^{4}+6 x^{3}-11 x^{2}+18 x -17}+11\right )}{4}\) | \(91\) |
elliptic | \(\text {Expression too large to display}\) | \(1609\) |
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Time = 0.28 (sec) , antiderivative size = 50, normalized size of antiderivative = 0.91 \[ \int \frac {x}{\sqrt {-17+18 x-11 x^2+6 x^3+x^4}} \, dx=\frac {1}{4} \, \log \left (2 \, x^{4} + 24 \, x^{3} + 68 \, x^{2} + 2 \, \sqrt {x^{4} + 6 \, x^{3} - 11 \, x^{2} + 18 \, x - 17} {\left (x^{2} + 9 \, x + 17\right )} + 11\right ) \]
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\[ \int \frac {x}{\sqrt {-17+18 x-11 x^2+6 x^3+x^4}} \, dx=\int \frac {x}{\sqrt {x^{4} + 6 x^{3} - 11 x^{2} + 18 x - 17}}\, dx \]
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\[ \int \frac {x}{\sqrt {-17+18 x-11 x^2+6 x^3+x^4}} \, dx=\int { \frac {x}{\sqrt {x^{4} + 6 \, x^{3} - 11 \, x^{2} + 18 \, x - 17}} \,d x } \]
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\[ \int \frac {x}{\sqrt {-17+18 x-11 x^2+6 x^3+x^4}} \, dx=\int { \frac {x}{\sqrt {x^{4} + 6 \, x^{3} - 11 \, x^{2} + 18 \, x - 17}} \,d x } \]
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Timed out. \[ \int \frac {x}{\sqrt {-17+18 x-11 x^2+6 x^3+x^4}} \, dx=\int \frac {x}{\sqrt {x^4+6\,x^3-11\,x^2+18\,x-17}} \,d x \]
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