3.87.4 \(\int \frac {6 x^2-6 x^2 \log (x)+4 e^6 x \log ^3(x)+(3 x^2 \log (x)+e^6 (-64-4 x) \log ^3(x)) \log (\frac {-45 x^2+e^6 (960+60 x) \log ^2(x)}{4 e^6 \log ^2(x)})}{-3 x^4 \log (x)+e^6 (64 x^2+4 x^3) \log ^3(x)} \, dx\)

Optimal. Leaf size=24 \[ \frac {\log \left (15 \left (16+x-\frac {3 x^2}{4 e^6 \log ^2(x)}\right )\right )}{x} \]

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Rubi [F]  time = 11.60, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {6 x^2-6 x^2 \log (x)+4 e^6 x \log ^3(x)+\left (3 x^2 \log (x)+e^6 (-64-4 x) \log ^3(x)\right ) \log \left (\frac {-45 x^2+e^6 (960+60 x) \log ^2(x)}{4 e^6 \log ^2(x)}\right )}{-3 x^4 \log (x)+e^6 \left (64 x^2+4 x^3\right ) \log ^3(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(6*x^2 - 6*x^2*Log[x] + 4*E^6*x*Log[x]^3 + (3*x^2*Log[x] + E^6*(-64 - 4*x)*Log[x]^3)*Log[(-45*x^2 + E^6*(9
60 + 60*x)*Log[x]^2)/(4*E^6*Log[x]^2)])/(-3*x^4*Log[x] + E^6*(64*x^2 + 4*x^3)*Log[x]^3),x]

[Out]

-2*ExpIntegralEi[-Log[x]] + Log[x]/16 - Log[16 + x]/16 + 3*Defer[Int][(3*x^2 - 4*E^6*(16 + x)*Log[x]^2)^(-1),
x] + 48*Defer[Int][1/((16 + x)*(3*x^2 - 4*E^6*(16 + x)*Log[x]^2)), x] - (E^6*Defer[Int][(x*Log[x])/(3*x^2 - 4*
E^6*(16 + x)*Log[x]^2), x])/32 - (E^6*Defer[Int][(x*Log[x])/(-3*x^2 + 4*E^6*(16 + x)*Log[x]^2), x])/32 + 8*E^6
*Defer[Int][Log[x]/(-3*x^3 + 4*E^6*x*(16 + x)*Log[x]^2), x] + 128*E^6*Defer[Int][Log[x]/(-3*x^4 + 4*E^6*x^2*(1
6 + x)*Log[x]^2), x] - Defer[Int][Log[15*(16 + x) - (45*x^2)/(4*E^6*Log[x]^2)]/x^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2 \left (-3 x+3 x \log (x)-2 e^6 \log ^3(x)\right )}{x \log (x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )}-\frac {\log \left (15 (16+x)-\frac {45 x^2}{4 e^6 \log ^2(x)}\right )}{x^2}\right ) \, dx\\ &=2 \int \frac {-3 x+3 x \log (x)-2 e^6 \log ^3(x)}{x \log (x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )} \, dx-\int \frac {\log \left (15 (16+x)-\frac {45 x^2}{4 e^6 \log ^2(x)}\right )}{x^2} \, dx\\ &=2 \int \frac {-3 x+3 x \log (x)-2 e^6 \log ^3(x)}{3 x^3 \log (x)-4 e^6 x (16+x) \log ^3(x)} \, dx-\int \frac {\log \left (15 (16+x)-\frac {45 x^2}{4 e^6 \log ^2(x)}\right )}{x^2} \, dx\\ &=2 \int \left (\frac {1}{2 x (16+x)}-\frac {1}{x^2 \log (x)}+\frac {96 x^2+3 x^3-2048 e^6 \log (x)-256 e^6 x \log (x)-8 e^6 x^2 \log (x)}{2 x^2 (16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )}\right ) \, dx-\int \frac {\log \left (15 (16+x)-\frac {45 x^2}{4 e^6 \log ^2(x)}\right )}{x^2} \, dx\\ &=-\left (2 \int \frac {1}{x^2 \log (x)} \, dx\right )+\int \frac {1}{x (16+x)} \, dx+\int \frac {96 x^2+3 x^3-2048 e^6 \log (x)-256 e^6 x \log (x)-8 e^6 x^2 \log (x)}{x^2 (16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )} \, dx-\int \frac {\log \left (15 (16+x)-\frac {45 x^2}{4 e^6 \log ^2(x)}\right )}{x^2} \, dx\\ &=\frac {1}{16} \int \frac {1}{x} \, dx-\frac {1}{16} \int \frac {1}{16+x} \, dx-2 \operatorname {Subst}\left (\int \frac {e^{-x}}{x} \, dx,x,\log (x)\right )+\int \frac {3 x^2 (32+x)-8 e^6 (16+x)^2 \log (x)}{x^2 (16+x) \left (3 x^2-4 e^6 (16+x) \log ^2(x)\right )} \, dx-\int \frac {\log \left (15 (16+x)-\frac {45 x^2}{4 e^6 \log ^2(x)}\right )}{x^2} \, dx\\ &=-2 \text {Ei}(-\log (x))+\frac {\log (x)}{16}-\frac {1}{16} \log (16+x)+\int \left (\frac {96 x^2+3 x^3-2048 e^6 \log (x)-256 e^6 x \log (x)-8 e^6 x^2 \log (x)}{16 x^2 \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )}+\frac {96 x^2+3 x^3-2048 e^6 \log (x)-256 e^6 x \log (x)-8 e^6 x^2 \log (x)}{256 (16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )}+\frac {-96 x^2-3 x^3+2048 e^6 \log (x)+256 e^6 x \log (x)+8 e^6 x^2 \log (x)}{256 x \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )}\right ) \, dx-\int \frac {\log \left (15 (16+x)-\frac {45 x^2}{4 e^6 \log ^2(x)}\right )}{x^2} \, dx\\ &=-2 \text {Ei}(-\log (x))+\frac {\log (x)}{16}-\frac {1}{16} \log (16+x)+\frac {1}{256} \int \frac {96 x^2+3 x^3-2048 e^6 \log (x)-256 e^6 x \log (x)-8 e^6 x^2 \log (x)}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )} \, dx+\frac {1}{256} \int \frac {-96 x^2-3 x^3+2048 e^6 \log (x)+256 e^6 x \log (x)+8 e^6 x^2 \log (x)}{x \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )} \, dx+\frac {1}{16} \int \frac {96 x^2+3 x^3-2048 e^6 \log (x)-256 e^6 x \log (x)-8 e^6 x^2 \log (x)}{x^2 \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )} \, dx-\int \frac {\log \left (15 (16+x)-\frac {45 x^2}{4 e^6 \log ^2(x)}\right )}{x^2} \, dx\\ &=-2 \text {Ei}(-\log (x))+\frac {\log (x)}{16}-\frac {1}{16} \log (16+x)+\frac {1}{256} \int \frac {3 x^2 (32+x)-8 e^6 (16+x)^2 \log (x)}{(16+x) \left (3 x^2-4 e^6 (16+x) \log ^2(x)\right )} \, dx+\frac {1}{256} \int \frac {-3 x^2 (32+x)+8 e^6 (16+x)^2 \log (x)}{3 x^3-4 e^6 x (16+x) \log ^2(x)} \, dx+\frac {1}{16} \int \frac {3 x^2 (32+x)-8 e^6 (16+x)^2 \log (x)}{3 x^4-4 e^6 x^2 (16+x) \log ^2(x)} \, dx-\int \frac {\log \left (15 (16+x)-\frac {45 x^2}{4 e^6 \log ^2(x)}\right )}{x^2} \, dx\\ &=-2 \text {Ei}(-\log (x))+\frac {\log (x)}{16}-\frac {1}{16} \log (16+x)+\frac {1}{256} \int \left (\frac {96 x^2}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )}+\frac {3 x^3}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )}-\frac {2048 e^6 \log (x)}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )}-\frac {256 e^6 x \log (x)}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )}-\frac {8 e^6 x^2 \log (x)}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )}\right ) \, dx+\frac {1}{256} \int \left (-\frac {96 x}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)}-\frac {3 x^2}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)}-\frac {256 e^6 \log (x)}{-3 x^2+64 e^6 \log ^2(x)+4 e^6 x \log ^2(x)}-\frac {2048 e^6 \log (x)}{x \left (-3 x^2+64 e^6 \log ^2(x)+4 e^6 x \log ^2(x)\right )}-\frac {8 e^6 x \log (x)}{-3 x^2+64 e^6 \log ^2(x)+4 e^6 x \log ^2(x)}\right ) \, dx+\frac {1}{16} \int \left (\frac {96}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)}+\frac {3 x}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)}+\frac {8 e^6 \log (x)}{-3 x^2+64 e^6 \log ^2(x)+4 e^6 x \log ^2(x)}+\frac {2048 e^6 \log (x)}{x^2 \left (-3 x^2+64 e^6 \log ^2(x)+4 e^6 x \log ^2(x)\right )}+\frac {256 e^6 \log (x)}{x \left (-3 x^2+64 e^6 \log ^2(x)+4 e^6 x \log ^2(x)\right )}\right ) \, dx-\int \frac {\log \left (15 (16+x)-\frac {45 x^2}{4 e^6 \log ^2(x)}\right )}{x^2} \, dx\\ &=-2 \text {Ei}(-\log (x))+\frac {\log (x)}{16}-\frac {1}{16} \log (16+x)-\frac {3}{256} \int \frac {x^2}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)} \, dx+\frac {3}{256} \int \frac {x^3}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )} \, dx+\frac {3}{16} \int \frac {x}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)} \, dx-\frac {3}{8} \int \frac {x}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)} \, dx+\frac {3}{8} \int \frac {x^2}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )} \, dx+6 \int \frac {1}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)} \, dx-\frac {1}{32} e^6 \int \frac {x^2 \log (x)}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )} \, dx-\frac {1}{32} e^6 \int \frac {x \log (x)}{-3 x^2+64 e^6 \log ^2(x)+4 e^6 x \log ^2(x)} \, dx+\frac {1}{2} e^6 \int \frac {\log (x)}{-3 x^2+64 e^6 \log ^2(x)+4 e^6 x \log ^2(x)} \, dx-e^6 \int \frac {x \log (x)}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )} \, dx-e^6 \int \frac {\log (x)}{-3 x^2+64 e^6 \log ^2(x)+4 e^6 x \log ^2(x)} \, dx-\left (8 e^6\right ) \int \frac {\log (x)}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )} \, dx-\left (8 e^6\right ) \int \frac {\log (x)}{x \left (-3 x^2+64 e^6 \log ^2(x)+4 e^6 x \log ^2(x)\right )} \, dx+\left (16 e^6\right ) \int \frac {\log (x)}{x \left (-3 x^2+64 e^6 \log ^2(x)+4 e^6 x \log ^2(x)\right )} \, dx+\left (128 e^6\right ) \int \frac {\log (x)}{x^2 \left (-3 x^2+64 e^6 \log ^2(x)+4 e^6 x \log ^2(x)\right )} \, dx-\int \frac {\log \left (15 (16+x)-\frac {45 x^2}{4 e^6 \log ^2(x)}\right )}{x^2} \, dx\\ &=-2 \text {Ei}(-\log (x))+\frac {\log (x)}{16}-\frac {1}{16} \log (16+x)-\frac {3}{256} \int \frac {x^2}{3 x^2-4 e^6 (16+x) \log ^2(x)} \, dx+\frac {3}{256} \int \frac {x^3}{(16+x) \left (3 x^2-4 e^6 (16+x) \log ^2(x)\right )} \, dx+\frac {3}{16} \int \frac {x}{3 x^2-4 e^6 (16+x) \log ^2(x)} \, dx-\frac {3}{8} \int \frac {x}{3 x^2-4 e^6 (16+x) \log ^2(x)} \, dx+\frac {3}{8} \int \frac {x^2}{(16+x) \left (3 x^2-4 e^6 (16+x) \log ^2(x)\right )} \, dx+6 \int \frac {1}{3 x^2-4 e^6 (16+x) \log ^2(x)} \, dx-\frac {1}{32} e^6 \int \frac {x^2 \log (x)}{(16+x) \left (3 x^2-4 e^6 (16+x) \log ^2(x)\right )} \, dx-\frac {1}{32} e^6 \int \frac {x \log (x)}{-3 x^2+4 e^6 (16+x) \log ^2(x)} \, dx+\frac {1}{2} e^6 \int \frac {\log (x)}{-3 x^2+4 e^6 (16+x) \log ^2(x)} \, dx-e^6 \int \frac {x \log (x)}{(16+x) \left (3 x^2-4 e^6 (16+x) \log ^2(x)\right )} \, dx-e^6 \int \frac {\log (x)}{-3 x^2+4 e^6 (16+x) \log ^2(x)} \, dx-\left (8 e^6\right ) \int \frac {\log (x)}{(16+x) \left (3 x^2-4 e^6 (16+x) \log ^2(x)\right )} \, dx-\left (8 e^6\right ) \int \frac {\log (x)}{-3 x^3+4 e^6 x (16+x) \log ^2(x)} \, dx+\left (16 e^6\right ) \int \frac {\log (x)}{-3 x^3+4 e^6 x (16+x) \log ^2(x)} \, dx+\left (128 e^6\right ) \int \frac {\log (x)}{-3 x^4+4 e^6 x^2 (16+x) \log ^2(x)} \, dx-\int \frac {\log \left (15 (16+x)-\frac {45 x^2}{4 e^6 \log ^2(x)}\right )}{x^2} \, dx\\ &=-2 \text {Ei}(-\log (x))+\frac {\log (x)}{16}-\frac {1}{16} \log (16+x)-\frac {3}{256} \int \frac {x^2}{3 x^2-4 e^6 (16+x) \log ^2(x)} \, dx+\frac {3}{256} \int \left (\frac {256}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)}-\frac {16 x}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)}+\frac {x^2}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)}-\frac {4096}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )}\right ) \, dx+\frac {3}{16} \int \frac {x}{3 x^2-4 e^6 (16+x) \log ^2(x)} \, dx-\frac {3}{8} \int \frac {x}{3 x^2-4 e^6 (16+x) \log ^2(x)} \, dx+\frac {3}{8} \int \left (-\frac {16}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)}+\frac {x}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)}+\frac {256}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )}\right ) \, dx+6 \int \frac {1}{3 x^2-4 e^6 (16+x) \log ^2(x)} \, dx-\frac {1}{32} e^6 \int \frac {x \log (x)}{-3 x^2+4 e^6 (16+x) \log ^2(x)} \, dx-\frac {1}{32} e^6 \int \left (\frac {x \log (x)}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)}+\frac {256 \log (x)}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )}+\frac {16 \log (x)}{-3 x^2+64 e^6 \log ^2(x)+4 e^6 x \log ^2(x)}\right ) \, dx+\frac {1}{2} e^6 \int \frac {\log (x)}{-3 x^2+4 e^6 (16+x) \log ^2(x)} \, dx-e^6 \int \frac {\log (x)}{-3 x^2+4 e^6 (16+x) \log ^2(x)} \, dx-e^6 \int \left (-\frac {16 \log (x)}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )}-\frac {\log (x)}{-3 x^2+64 e^6 \log ^2(x)+4 e^6 x \log ^2(x)}\right ) \, dx-\left (8 e^6\right ) \int \frac {\log (x)}{(16+x) \left (3 x^2-4 e^6 (16+x) \log ^2(x)\right )} \, dx-\left (8 e^6\right ) \int \frac {\log (x)}{-3 x^3+4 e^6 x (16+x) \log ^2(x)} \, dx+\left (16 e^6\right ) \int \frac {\log (x)}{-3 x^3+4 e^6 x (16+x) \log ^2(x)} \, dx+\left (128 e^6\right ) \int \frac {\log (x)}{-3 x^4+4 e^6 x^2 (16+x) \log ^2(x)} \, dx-\int \frac {\log \left (15 (16+x)-\frac {45 x^2}{4 e^6 \log ^2(x)}\right )}{x^2} \, dx\\ &=-2 \text {Ei}(-\log (x))+\frac {\log (x)}{16}-\frac {1}{16} \log (16+x)+\frac {3}{256} \int \frac {x^2}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)} \, dx-\frac {3}{256} \int \frac {x^2}{3 x^2-4 e^6 (16+x) \log ^2(x)} \, dx-\frac {3}{16} \int \frac {x}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)} \, dx+\frac {3}{16} \int \frac {x}{3 x^2-4 e^6 (16+x) \log ^2(x)} \, dx+\frac {3}{8} \int \frac {x}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)} \, dx-\frac {3}{8} \int \frac {x}{3 x^2-4 e^6 (16+x) \log ^2(x)} \, dx+3 \int \frac {1}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)} \, dx-6 \int \frac {1}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)} \, dx+6 \int \frac {1}{3 x^2-4 e^6 (16+x) \log ^2(x)} \, dx-48 \int \frac {1}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )} \, dx+96 \int \frac {1}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )} \, dx-\frac {1}{32} e^6 \int \frac {x \log (x)}{3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)} \, dx-\frac {1}{32} e^6 \int \frac {x \log (x)}{-3 x^2+4 e^6 (16+x) \log ^2(x)} \, dx-\frac {1}{2} e^6 \int \frac {\log (x)}{-3 x^2+64 e^6 \log ^2(x)+4 e^6 x \log ^2(x)} \, dx+\frac {1}{2} e^6 \int \frac {\log (x)}{-3 x^2+4 e^6 (16+x) \log ^2(x)} \, dx+e^6 \int \frac {\log (x)}{-3 x^2+64 e^6 \log ^2(x)+4 e^6 x \log ^2(x)} \, dx-e^6 \int \frac {\log (x)}{-3 x^2+4 e^6 (16+x) \log ^2(x)} \, dx-\left (8 e^6\right ) \int \frac {\log (x)}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )} \, dx-\left (8 e^6\right ) \int \frac {\log (x)}{(16+x) \left (3 x^2-4 e^6 (16+x) \log ^2(x)\right )} \, dx-\left (8 e^6\right ) \int \frac {\log (x)}{-3 x^3+4 e^6 x (16+x) \log ^2(x)} \, dx+\left (16 e^6\right ) \int \frac {\log (x)}{(16+x) \left (3 x^2-64 e^6 \log ^2(x)-4 e^6 x \log ^2(x)\right )} \, dx+\left (16 e^6\right ) \int \frac {\log (x)}{-3 x^3+4 e^6 x (16+x) \log ^2(x)} \, dx+\left (128 e^6\right ) \int \frac {\log (x)}{-3 x^4+4 e^6 x^2 (16+x) \log ^2(x)} \, dx-\int \frac {\log \left (15 (16+x)-\frac {45 x^2}{4 e^6 \log ^2(x)}\right )}{x^2} \, dx\\ &=-2 \text {Ei}(-\log (x))+\frac {\log (x)}{16}-\frac {1}{16} \log (16+x)+3 \int \frac {1}{3 x^2-4 e^6 (16+x) \log ^2(x)} \, dx-48 \int \frac {1}{(16+x) \left (3 x^2-4 e^6 (16+x) \log ^2(x)\right )} \, dx+96 \int \frac {1}{(16+x) \left (3 x^2-4 e^6 (16+x) \log ^2(x)\right )} \, dx-\frac {1}{32} e^6 \int \frac {x \log (x)}{3 x^2-4 e^6 (16+x) \log ^2(x)} \, dx-\frac {1}{32} e^6 \int \frac {x \log (x)}{-3 x^2+4 e^6 (16+x) \log ^2(x)} \, dx-2 \left (\left (8 e^6\right ) \int \frac {\log (x)}{(16+x) \left (3 x^2-4 e^6 (16+x) \log ^2(x)\right )} \, dx\right )-\left (8 e^6\right ) \int \frac {\log (x)}{-3 x^3+4 e^6 x (16+x) \log ^2(x)} \, dx+\left (16 e^6\right ) \int \frac {\log (x)}{(16+x) \left (3 x^2-4 e^6 (16+x) \log ^2(x)\right )} \, dx+\left (16 e^6\right ) \int \frac {\log (x)}{-3 x^3+4 e^6 x (16+x) \log ^2(x)} \, dx+\left (128 e^6\right ) \int \frac {\log (x)}{-3 x^4+4 e^6 x^2 (16+x) \log ^2(x)} \, dx-\int \frac {\log \left (15 (16+x)-\frac {45 x^2}{4 e^6 \log ^2(x)}\right )}{x^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.10, size = 25, normalized size = 1.04 \begin {gather*} \frac {\log \left (15 (16+x)-\frac {45 x^2}{4 e^6 \log ^2(x)}\right )}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(6*x^2 - 6*x^2*Log[x] + 4*E^6*x*Log[x]^3 + (3*x^2*Log[x] + E^6*(-64 - 4*x)*Log[x]^3)*Log[(-45*x^2 +
E^6*(960 + 60*x)*Log[x]^2)/(4*E^6*Log[x]^2)])/(-3*x^4*Log[x] + E^6*(64*x^2 + 4*x^3)*Log[x]^3),x]

[Out]

Log[15*(16 + x) - (45*x^2)/(4*E^6*Log[x]^2)]/x

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fricas [A]  time = 0.93, size = 30, normalized size = 1.25 \begin {gather*} \frac {\log \left (\frac {15 \, {\left (4 \, {\left (x + 16\right )} e^{6} \log \relax (x)^{2} - 3 \, x^{2}\right )} e^{\left (-6\right )}}{4 \, \log \relax (x)^{2}}\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x-64)*exp(3)^2*log(x)^3+3*x^2*log(x))*log(1/4*((60*x+960)*exp(3)^2*log(x)^2-45*x^2)/exp(3)^2/l
og(x)^2)+4*x*exp(3)^2*log(x)^3-6*x^2*log(x)+6*x^2)/((4*x^3+64*x^2)*exp(3)^2*log(x)^3-3*x^4*log(x)),x, algorith
m="fricas")

[Out]

log(15/4*(4*(x + 16)*e^6*log(x)^2 - 3*x^2)*e^(-6)/log(x)^2)/x

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giac [A]  time = 0.40, size = 39, normalized size = 1.62 \begin {gather*} \frac {\log \left (60 \, x e^{6} \log \relax (x)^{2} + 960 \, e^{6} \log \relax (x)^{2} - 45 \, x^{2}\right ) - \log \left (4 \, \log \relax (x)^{2}\right ) - 6}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x-64)*exp(3)^2*log(x)^3+3*x^2*log(x))*log(1/4*((60*x+960)*exp(3)^2*log(x)^2-45*x^2)/exp(3)^2/l
og(x)^2)+4*x*exp(3)^2*log(x)^3-6*x^2*log(x)+6*x^2)/((4*x^3+64*x^2)*exp(3)^2*log(x)^3-3*x^4*log(x)),x, algorith
m="giac")

[Out]

(log(60*x*e^6*log(x)^2 + 960*e^6*log(x)^2 - 45*x^2) - log(4*log(x)^2) - 6)/x

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maple [C]  time = 0.61, size = 313, normalized size = 13.04

method	result	size
risch	\(\frac {\ln \left (\left (x \ln \relax (x )^{2}+16 \ln \relax (x )^{2}\right ) {\mathrm e}^{6}-\frac {3 x^{2}}{4}\right )}{x}+\frac {i \pi \mathrm {csgn}\left (i \ln \relax (x )\right )^{2} \mathrm {csgn}\left (i \ln \relax (x )^{2}\right )-2 i \pi \,\mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i \ln \relax (x )^{2}\right )^{2}+i \pi \,\mathrm {csgn}\left (i \left (\left (x \ln \relax (x )^{2}+16 \ln \relax (x )^{2}\right ) {\mathrm e}^{6}-\frac {3 x^{2}}{4}\right )\right ) \mathrm {csgn}\left (\frac {i \left (\left (x \ln \relax (x )^{2}+16 \ln \relax (x )^{2}\right ) {\mathrm e}^{6}-\frac {3 x^{2}}{4}\right )}{\ln \relax (x )^{2}}\right )^{2}-i \pi \,\mathrm {csgn}\left (i \left (\left (x \ln \relax (x )^{2}+16 \ln \relax (x )^{2}\right ) {\mathrm e}^{6}-\frac {3 x^{2}}{4}\right )\right ) \mathrm {csgn}\left (\frac {i \left (\left (x \ln \relax (x )^{2}+16 \ln \relax (x )^{2}\right ) {\mathrm e}^{6}-\frac {3 x^{2}}{4}\right )}{\ln \relax (x )^{2}}\right ) \mathrm {csgn}\left (\frac {i}{\ln \relax (x )^{2}}\right )-12+i \pi \mathrm {csgn}\left (\frac {i \left (\left (x \ln \relax (x )^{2}+16 \ln \relax (x )^{2}\right ) {\mathrm e}^{6}-\frac {3 x^{2}}{4}\right )}{\ln \relax (x )^{2}}\right )^{2} \mathrm {csgn}\left (\frac {i}{\ln \relax (x )^{2}}\right )-i \pi \mathrm {csgn}\left (\frac {i \left (\left (x \ln \relax (x )^{2}+16 \ln \relax (x )^{2}\right ) {\mathrm e}^{6}-\frac {3 x^{2}}{4}\right )}{\ln \relax (x )^{2}}\right )^{3}+i \pi \mathrm {csgn}\left (i \ln \relax (x )^{2}\right )^{3}+2 \ln \relax (3)+2 \ln \relax (5)-4 \ln \left (\ln \relax (x )\right )}{2 x}\)	\(313\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-4*x-64)*exp(3)^2*ln(x)^3+3*x^2*ln(x))*ln(1/4*((60*x+960)*exp(3)^2*ln(x)^2-45*x^2)/exp(3)^2/ln(x)^2)+4*
x*exp(3)^2*ln(x)^3-6*x^2*ln(x)+6*x^2)/((4*x^3+64*x^2)*exp(3)^2*ln(x)^3-3*x^4*ln(x)),x,method=_RETURNVERBOSE)

[Out]

1/x*ln((x*ln(x)^2+16*ln(x)^2)*exp(6)-3/4*x^2)+1/2*(I*Pi*csgn(I*ln(x))^2*csgn(I*ln(x)^2)-2*I*Pi*csgn(I*ln(x))*c
sgn(I*ln(x)^2)^2+I*Pi*csgn(I*((x*ln(x)^2+16*ln(x)^2)*exp(6)-3/4*x^2))*csgn(I/ln(x)^2*((x*ln(x)^2+16*ln(x)^2)*e
xp(6)-3/4*x^2))^2-I*Pi*csgn(I*((x*ln(x)^2+16*ln(x)^2)*exp(6)-3/4*x^2))*csgn(I/ln(x)^2*((x*ln(x)^2+16*ln(x)^2)*
exp(6)-3/4*x^2))*csgn(I/ln(x)^2)-12+I*Pi*csgn(I/ln(x)^2*((x*ln(x)^2+16*ln(x)^2)*exp(6)-3/4*x^2))^2*csgn(I/ln(x
)^2)-I*Pi*csgn(I/ln(x)^2*((x*ln(x)^2+16*ln(x)^2)*exp(6)-3/4*x^2))^3+I*Pi*csgn(I*ln(x)^2)^3+2*ln(3)+2*ln(5)-4*l
n(ln(x)))/x

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maxima [A]  time = 0.49, size = 41, normalized size = 1.71 \begin {gather*} \frac {\log \relax (5) + \log \relax (3) - 2 \, \log \relax (2) + \log \left (4 \, {\left (x e^{6} + 16 \, e^{6}\right )} \log \relax (x)^{2} - 3 \, x^{2}\right ) - 2 \, \log \left (\log \relax (x)\right ) - 6}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x-64)*exp(3)^2*log(x)^3+3*x^2*log(x))*log(1/4*((60*x+960)*exp(3)^2*log(x)^2-45*x^2)/exp(3)^2/l
og(x)^2)+4*x*exp(3)^2*log(x)^3-6*x^2*log(x)+6*x^2)/((4*x^3+64*x^2)*exp(3)^2*log(x)^3-3*x^4*log(x)),x, algorith
m="maxima")

[Out]

(log(5) + log(3) - 2*log(2) + log(4*(x*e^6 + 16*e^6)*log(x)^2 - 3*x^2) - 2*log(log(x)) - 6)/x

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mupad [B]  time = 5.78, size = 32, normalized size = 1.33 \begin {gather*} \frac {\ln \left (-\frac {\frac {45\,x^2}{4}-\frac {{\mathrm {e}}^6\,{\ln \relax (x)}^2\,\left (60\,x+960\right )}{4}}{{\ln \relax (x)}^2}\right )-6}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(-(exp(-6)*((45*x^2)/4 - (exp(6)*log(x)^2*(60*x + 960))/4))/log(x)^2)*(3*x^2*log(x) - exp(6)*log(x)^3
*(4*x + 64)) - 6*x^2*log(x) + 6*x^2 + 4*x*exp(6)*log(x)^3)/(3*x^4*log(x) - exp(6)*log(x)^3*(64*x^2 + 4*x^3)),x
)

[Out]

(log(-((45*x^2)/4 - (exp(6)*log(x)^2*(60*x + 960))/4)/log(x)^2) - 6)/x

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sympy [A]  time = 0.62, size = 32, normalized size = 1.33 \begin {gather*} \frac {\log {\left (\frac {- \frac {45 x^{2}}{4} + \frac {\left (60 x + 960\right ) e^{6} \log {\relax (x )}^{2}}{4}}{e^{6} \log {\relax (x )}^{2}} \right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x-64)*exp(3)**2*ln(x)**3+3*x**2*ln(x))*ln(1/4*((60*x+960)*exp(3)**2*ln(x)**2-45*x**2)/exp(3)**
2/ln(x)**2)+4*x*exp(3)**2*ln(x)**3-6*x**2*ln(x)+6*x**2)/((4*x**3+64*x**2)*exp(3)**2*ln(x)**3-3*x**4*ln(x)),x)

[Out]

log((-45*x**2/4 + (60*x + 960)*exp(6)*log(x)**2/4)*exp(-6)/log(x)**2)/x

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