Integrand size = 26, antiderivative size = 56 \[ \int \frac {-1+x}{\sqrt {4-16 x+12 x^2-8 x^3+x^4}} \, dx=-\frac {1}{4} \log \left (36-56 x+44 x^2-12 x^3+x^4+\left (-14+8 x-x^2\right ) \sqrt {4-16 x+12 x^2-8 x^3+x^4}\right ) \]
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\[ \int \frac {-1+x}{\sqrt {4-16 x+12 x^2-8 x^3+x^4}} \, dx=\int \frac {-1+x}{\sqrt {4-16 x+12 x^2-8 x^3+x^4}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {1}{\sqrt {4-16 x+12 x^2-8 x^3+x^4}}+\frac {x}{\sqrt {4-16 x+12 x^2-8 x^3+x^4}}\right ) \, dx \\ & = -\int \frac {1}{\sqrt {4-16 x+12 x^2-8 x^3+x^4}} \, dx+\int \frac {x}{\sqrt {4-16 x+12 x^2-8 x^3+x^4}} \, dx \\ \end{align*}
Time = 3.98 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.00 \[ \int \frac {-1+x}{\sqrt {4-16 x+12 x^2-8 x^3+x^4}} \, dx=-\frac {1}{4} \log \left (36-56 x+44 x^2-12 x^3+x^4+\left (-14+8 x-x^2\right ) \sqrt {4-16 x+12 x^2-8 x^3+x^4}\right ) \]
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Time = 1.28 (sec) , antiderivative size = 92, normalized size of antiderivative = 1.64
method | result | size |
trager | \(-\frac {\ln \left (x^{4}-\sqrt {x^{4}-8 x^{3}+12 x^{2}-16 x +4}\, x^{2}-12 x^{3}+8 x \sqrt {x^{4}-8 x^{3}+12 x^{2}-16 x +4}+44 x^{2}-14 \sqrt {x^{4}-8 x^{3}+12 x^{2}-16 x +4}-56 x +36\right )}{4}\) | \(92\) |
default | \(\text {Expression too large to display}\) | \(2700\) |
elliptic | \(\text {Expression too large to display}\) | \(2700\) |
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Time = 0.28 (sec) , antiderivative size = 53, normalized size of antiderivative = 0.95 \[ \int \frac {-1+x}{\sqrt {4-16 x+12 x^2-8 x^3+x^4}} \, dx=\frac {1}{4} \, \log \left (-x^{4} + 12 \, x^{3} - 44 \, x^{2} - \sqrt {x^{4} - 8 \, x^{3} + 12 \, x^{2} - 16 \, x + 4} {\left (x^{2} - 8 \, x + 14\right )} + 56 \, x - 36\right ) \]
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\[ \int \frac {-1+x}{\sqrt {4-16 x+12 x^2-8 x^3+x^4}} \, dx=\int \frac {x - 1}{\sqrt {x^{4} - 8 x^{3} + 12 x^{2} - 16 x + 4}}\, dx \]
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\[ \int \frac {-1+x}{\sqrt {4-16 x+12 x^2-8 x^3+x^4}} \, dx=\int { \frac {x - 1}{\sqrt {x^{4} - 8 \, x^{3} + 12 \, x^{2} - 16 \, x + 4}} \,d x } \]
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\[ \int \frac {-1+x}{\sqrt {4-16 x+12 x^2-8 x^3+x^4}} \, dx=\int { \frac {x - 1}{\sqrt {x^{4} - 8 \, x^{3} + 12 \, x^{2} - 16 \, x + 4}} \,d x } \]
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Timed out. \[ \int \frac {-1+x}{\sqrt {4-16 x+12 x^2-8 x^3+x^4}} \, dx=\int \frac {x-1}{\sqrt {x^4-8\,x^3+12\,x^2-16\,x+4}} \,d x \]
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