Integrand size = 199, antiderivative size = 28 \[ \int \frac {-4+4 x+60 x^2-448 x^3+\left (-12 x-64 x^2\right ) \log (x)+\left (32+136 x-336 x^2+(-8-48 x) \log (x)\right ) \log (4-7 x-\log (x))}{-4 x^5-25 x^6-8 x^7+112 x^8+\left (x^5+8 x^6+16 x^7\right ) \log (x)+\left (-8 x^4-50 x^5-16 x^6+224 x^7+\left (2 x^4+16 x^5+32 x^6\right ) \log (x)\right ) \log (4-7 x-\log (x))+\left (-4 x^3-25 x^4-8 x^5+112 x^6+\left (x^3+8 x^4+16 x^5\right ) \log (x)\right ) \log ^2(4-7 x-\log (x))} \, dx=\frac {4}{x \left (x+4 x^2\right ) (x+\log (4-7 x-\log (x)))} \]
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\[ \int \frac {-4+4 x+60 x^2-448 x^3+\left (-12 x-64 x^2\right ) \log (x)+\left (32+136 x-336 x^2+(-8-48 x) \log (x)\right ) \log (4-7 x-\log (x))}{-4 x^5-25 x^6-8 x^7+112 x^8+\left (x^5+8 x^6+16 x^7\right ) \log (x)+\left (-8 x^4-50 x^5-16 x^6+224 x^7+\left (2 x^4+16 x^5+32 x^6\right ) \log (x)\right ) \log (4-7 x-\log (x))+\left (-4 x^3-25 x^4-8 x^5+112 x^6+\left (x^3+8 x^4+16 x^5\right ) \log (x)\right ) \log ^2(4-7 x-\log (x))} \, dx=\int \frac {-4+4 x+60 x^2-448 x^3+\left (-12 x-64 x^2\right ) \log (x)+\left (32+136 x-336 x^2+(-8-48 x) \log (x)\right ) \log (4-7 x-\log (x))}{-4 x^5-25 x^6-8 x^7+112 x^8+\left (x^5+8 x^6+16 x^7\right ) \log (x)+\left (-8 x^4-50 x^5-16 x^6+224 x^7+\left (2 x^4+16 x^5+32 x^6\right ) \log (x)\right ) \log (4-7 x-\log (x))+\left (-4 x^3-25 x^4-8 x^5+112 x^6+\left (x^3+8 x^4+16 x^5\right ) \log (x)\right ) \log ^2(4-7 x-\log (x))} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {4 \left (1-x-15 x^2+112 x^3+\left (-8-34 x+84 x^2\right ) \log (4-7 x-\log (x))+\log (x) (x (3+16 x)+2 (1+6 x) \log (4-7 x-\log (x)))\right )}{x^3 (1+4 x)^2 (4-7 x-\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx \\ & = 4 \int \frac {1-x-15 x^2+112 x^3+\left (-8-34 x+84 x^2\right ) \log (4-7 x-\log (x))+\log (x) (x (3+16 x)+2 (1+6 x) \log (4-7 x-\log (x)))}{x^3 (1+4 x)^2 (4-7 x-\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx \\ & = 4 \int \left (\frac {-1-3 x-7 x^2-x \log (x)}{x^3 (1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}-\frac {2 (1+6 x)}{x^3 (1+4 x)^2 (x+\log (4-7 x-\log (x)))}\right ) \, dx \\ & = 4 \int \frac {-1-3 x-7 x^2-x \log (x)}{x^3 (1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx-8 \int \frac {1+6 x}{x^3 (1+4 x)^2 (x+\log (4-7 x-\log (x)))} \, dx \\ & = 4 \int \left (\frac {-1-3 x-7 x^2-x \log (x)}{x^3 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}+\frac {4 \left (1+3 x+7 x^2+x \log (x)\right )}{x^2 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}-\frac {16 \left (1+3 x+7 x^2+x \log (x)\right )}{x (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}+\frac {64 \left (1+3 x+7 x^2+x \log (x)\right )}{(1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}\right ) \, dx-8 \int \left (\frac {1}{x^3 (x+\log (4-7 x-\log (x)))}-\frac {2}{x^2 (x+\log (4-7 x-\log (x)))}+\frac {32}{(1+4 x)^2 (x+\log (4-7 x-\log (x)))}\right ) \, dx \\ & = 4 \int \frac {-1-3 x-7 x^2-x \log (x)}{x^3 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx-8 \int \frac {1}{x^3 (x+\log (4-7 x-\log (x)))} \, dx+16 \int \frac {1+3 x+7 x^2+x \log (x)}{x^2 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+16 \int \frac {1}{x^2 (x+\log (4-7 x-\log (x)))} \, dx-64 \int \frac {1+3 x+7 x^2+x \log (x)}{x (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+256 \int \frac {1+3 x+7 x^2+x \log (x)}{(1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx-256 \int \frac {1}{(1+4 x)^2 (x+\log (4-7 x-\log (x)))} \, dx \\ & = \frac {64}{x+\log (4-7 x-\log (x))}+4 \int \left (-\frac {1}{x^3 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}-\frac {3}{x^2 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}-\frac {7}{x (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}-\frac {\log (x)}{x^2 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}\right ) \, dx-8 \int \frac {1}{x^3 (x+\log (4-7 x-\log (x)))} \, dx+16 \int \frac {1}{x^2 (x+\log (4-7 x-\log (x)))} \, dx+16 \int \left (\frac {7}{(-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}+\frac {1}{x^2 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}+\frac {3}{x (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}+\frac {\log (x)}{x (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}\right ) \, dx-256 \int \frac {1}{(1+4 x)^2 (x+\log (4-7 x-\log (x)))} \, dx+256 \int \left (\frac {1}{(1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}+\frac {3 x}{(1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}+\frac {7 x^2}{(1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}+\frac {x \log (x)}{(1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}\right ) \, dx \\ & = \frac {64}{x+\log (4-7 x-\log (x))}-4 \int \frac {1}{x^3 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx-4 \int \frac {\log (x)}{x^2 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx-8 \int \frac {1}{x^3 (x+\log (4-7 x-\log (x)))} \, dx-12 \int \frac {1}{x^2 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+16 \int \frac {1}{x^2 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+16 \int \frac {\log (x)}{x (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+16 \int \frac {1}{x^2 (x+\log (4-7 x-\log (x)))} \, dx-28 \int \frac {1}{x (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+48 \int \frac {1}{x (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+112 \int \frac {1}{(-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+256 \int \frac {1}{(1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+256 \int \frac {x \log (x)}{(1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx-256 \int \frac {1}{(1+4 x)^2 (x+\log (4-7 x-\log (x)))} \, dx+768 \int \frac {x}{(1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+1792 \int \frac {x^2}{(1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx \\ & = \frac {64}{x+\log (4-7 x-\log (x))}-4 \int \frac {1}{x^3 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx-4 \int \frac {\log (x)}{x^2 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx-8 \int \frac {1}{x^3 (x+\log (4-7 x-\log (x)))} \, dx-12 \int \frac {1}{x^2 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+16 \int \frac {1}{x^2 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+16 \int \frac {\log (x)}{x (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+16 \int \frac {1}{x^2 (x+\log (4-7 x-\log (x)))} \, dx-28 \int \frac {1}{x (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+48 \int \frac {1}{x (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+112 \int \frac {1}{(-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+256 \int \frac {1}{(1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx-256 \int \frac {1}{(1+4 x)^2 (x+\log (4-7 x-\log (x)))} \, dx+256 \int \left (\frac {\log (x)}{4 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}-\frac {\log (x)}{4 (1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}\right ) \, dx+768 \int \left (\frac {1}{4 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}-\frac {1}{4 (1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}\right ) \, dx+1792 \int \left (-\frac {1}{16 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}+\frac {x}{4 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}+\frac {1}{16 (1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2}\right ) \, dx \\ & = \frac {64}{x+\log (4-7 x-\log (x))}-4 \int \frac {1}{x^3 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx-4 \int \frac {\log (x)}{x^2 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx-8 \int \frac {1}{x^3 (x+\log (4-7 x-\log (x)))} \, dx-12 \int \frac {1}{x^2 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+16 \int \frac {1}{x^2 (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+16 \int \frac {\log (x)}{x (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+16 \int \frac {1}{x^2 (x+\log (4-7 x-\log (x)))} \, dx-28 \int \frac {1}{x (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+48 \int \frac {1}{x (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+64 \int \frac {\log (x)}{(-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx-64 \int \frac {\log (x)}{(1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+112 \int \frac {1}{(1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+192 \int \frac {1}{(-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx-192 \int \frac {1}{(1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx+256 \int \frac {1}{(1+4 x) (-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx-256 \int \frac {1}{(1+4 x)^2 (x+\log (4-7 x-\log (x)))} \, dx+448 \int \frac {x}{(-4+7 x+\log (x)) (x+\log (4-7 x-\log (x)))^2} \, dx \\ \end{align*}
Time = 0.09 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93 \[ \int \frac {-4+4 x+60 x^2-448 x^3+\left (-12 x-64 x^2\right ) \log (x)+\left (32+136 x-336 x^2+(-8-48 x) \log (x)\right ) \log (4-7 x-\log (x))}{-4 x^5-25 x^6-8 x^7+112 x^8+\left (x^5+8 x^6+16 x^7\right ) \log (x)+\left (-8 x^4-50 x^5-16 x^6+224 x^7+\left (2 x^4+16 x^5+32 x^6\right ) \log (x)\right ) \log (4-7 x-\log (x))+\left (-4 x^3-25 x^4-8 x^5+112 x^6+\left (x^3+8 x^4+16 x^5\right ) \log (x)\right ) \log ^2(4-7 x-\log (x))} \, dx=\frac {4}{x^2 (1+4 x) (x+\log (4-7 x-\log (x)))} \]
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Time = 5.82 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96
method | result | size |
default | \(\frac {4}{x^{2} \left (1+4 x \right ) \left (x +\ln \left (-\ln \left (x \right )-7 x +4\right )\right )}\) | \(27\) |
risch | \(\frac {4}{x^{2} \left (1+4 x \right ) \left (x +\ln \left (-\ln \left (x \right )-7 x +4\right )\right )}\) | \(27\) |
parallelrisch | \(\frac {4}{x^{2} \left (4 x \ln \left (-\ln \left (x \right )-7 x +4\right )+4 x^{2}+\ln \left (-\ln \left (x \right )-7 x +4\right )+x \right )}\) | \(38\) |
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Time = 0.25 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.18 \[ \int \frac {-4+4 x+60 x^2-448 x^3+\left (-12 x-64 x^2\right ) \log (x)+\left (32+136 x-336 x^2+(-8-48 x) \log (x)\right ) \log (4-7 x-\log (x))}{-4 x^5-25 x^6-8 x^7+112 x^8+\left (x^5+8 x^6+16 x^7\right ) \log (x)+\left (-8 x^4-50 x^5-16 x^6+224 x^7+\left (2 x^4+16 x^5+32 x^6\right ) \log (x)\right ) \log (4-7 x-\log (x))+\left (-4 x^3-25 x^4-8 x^5+112 x^6+\left (x^3+8 x^4+16 x^5\right ) \log (x)\right ) \log ^2(4-7 x-\log (x))} \, dx=\frac {4}{4 \, x^{4} + x^{3} + {\left (4 \, x^{3} + x^{2}\right )} \log \left (-7 \, x - \log \left (x\right ) + 4\right )} \]
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Time = 0.16 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96 \[ \int \frac {-4+4 x+60 x^2-448 x^3+\left (-12 x-64 x^2\right ) \log (x)+\left (32+136 x-336 x^2+(-8-48 x) \log (x)\right ) \log (4-7 x-\log (x))}{-4 x^5-25 x^6-8 x^7+112 x^8+\left (x^5+8 x^6+16 x^7\right ) \log (x)+\left (-8 x^4-50 x^5-16 x^6+224 x^7+\left (2 x^4+16 x^5+32 x^6\right ) \log (x)\right ) \log (4-7 x-\log (x))+\left (-4 x^3-25 x^4-8 x^5+112 x^6+\left (x^3+8 x^4+16 x^5\right ) \log (x)\right ) \log ^2(4-7 x-\log (x))} \, dx=\frac {4}{4 x^{4} + x^{3} + \left (4 x^{3} + x^{2}\right ) \log {\left (- 7 x - \log {\left (x \right )} + 4 \right )}} \]
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Time = 0.24 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.18 \[ \int \frac {-4+4 x+60 x^2-448 x^3+\left (-12 x-64 x^2\right ) \log (x)+\left (32+136 x-336 x^2+(-8-48 x) \log (x)\right ) \log (4-7 x-\log (x))}{-4 x^5-25 x^6-8 x^7+112 x^8+\left (x^5+8 x^6+16 x^7\right ) \log (x)+\left (-8 x^4-50 x^5-16 x^6+224 x^7+\left (2 x^4+16 x^5+32 x^6\right ) \log (x)\right ) \log (4-7 x-\log (x))+\left (-4 x^3-25 x^4-8 x^5+112 x^6+\left (x^3+8 x^4+16 x^5\right ) \log (x)\right ) \log ^2(4-7 x-\log (x))} \, dx=\frac {4}{4 \, x^{4} + x^{3} + {\left (4 \, x^{3} + x^{2}\right )} \log \left (-7 \, x - \log \left (x\right ) + 4\right )} \]
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Time = 0.38 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.50 \[ \int \frac {-4+4 x+60 x^2-448 x^3+\left (-12 x-64 x^2\right ) \log (x)+\left (32+136 x-336 x^2+(-8-48 x) \log (x)\right ) \log (4-7 x-\log (x))}{-4 x^5-25 x^6-8 x^7+112 x^8+\left (x^5+8 x^6+16 x^7\right ) \log (x)+\left (-8 x^4-50 x^5-16 x^6+224 x^7+\left (2 x^4+16 x^5+32 x^6\right ) \log (x)\right ) \log (4-7 x-\log (x))+\left (-4 x^3-25 x^4-8 x^5+112 x^6+\left (x^3+8 x^4+16 x^5\right ) \log (x)\right ) \log ^2(4-7 x-\log (x))} \, dx=\frac {4}{4 \, x^{4} + 4 \, x^{3} \log \left (-7 \, x - \log \left (x\right ) + 4\right ) + x^{3} + x^{2} \log \left (-7 \, x - \log \left (x\right ) + 4\right )} \]
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Time = 9.98 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93 \[ \int \frac {-4+4 x+60 x^2-448 x^3+\left (-12 x-64 x^2\right ) \log (x)+\left (32+136 x-336 x^2+(-8-48 x) \log (x)\right ) \log (4-7 x-\log (x))}{-4 x^5-25 x^6-8 x^7+112 x^8+\left (x^5+8 x^6+16 x^7\right ) \log (x)+\left (-8 x^4-50 x^5-16 x^6+224 x^7+\left (2 x^4+16 x^5+32 x^6\right ) \log (x)\right ) \log (4-7 x-\log (x))+\left (-4 x^3-25 x^4-8 x^5+112 x^6+\left (x^3+8 x^4+16 x^5\right ) \log (x)\right ) \log ^2(4-7 x-\log (x))} \, dx=\frac {4}{x^2\,\left (4\,x+1\right )\,\left (x+\ln \left (4-\ln \left (x\right )-7\,x\right )\right )} \]
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