3.19.24 \(\int \frac {e^{16} (-36-12 x^2+6 x^3)+e^{16} (54+18 x^2) \log (x)+(e^{16} (-27+3 x^2-9 x^3)-18 e^{16} x^2 \log (x)) \log (x^2)}{36 x+24 x^3-12 x^4+4 x^5-4 x^6+x^7+(-108 x-72 x^3+18 x^4-12 x^5+6 x^6) \log (x)+(81 x+54 x^3+9 x^5) \log ^2(x)} \, dx\)

Optimal. Leaf size=30 \[ \frac {e^{16} \log \left (x^2\right )}{-x+\left (3+x^2\right ) \left (\frac {1}{3} (-2+x)+\log (x)\right )} \]

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Rubi [F]  time = 7.65, 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 {e^{16} \left (-36-12 x^2+6 x^3\right )+e^{16} \left (54+18 x^2\right ) \log (x)+\left (e^{16} \left (-27+3 x^2-9 x^3\right )-18 e^{16} x^2 \log (x)\right ) \log \left (x^2\right )}{36 x+24 x^3-12 x^4+4 x^5-4 x^6+x^7+\left (-108 x-72 x^3+18 x^4-12 x^5+6 x^6\right ) \log (x)+\left (81 x+54 x^3+9 x^5\right ) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^16*(-36 - 12*x^2 + 6*x^3) + E^16*(54 + 18*x^2)*Log[x] + (E^16*(-27 + 3*x^2 - 9*x^3) - 18*E^16*x^2*Log[x
])*Log[x^2])/(36*x + 24*x^3 - 12*x^4 + 4*x^5 - 4*x^6 + x^7 + (-108*x - 72*x^3 + 18*x^4 - 12*x^5 + 6*x^6)*Log[x
] + (81*x + 54*x^3 + 9*x^5)*Log[x]^2),x]

[Out]

6*E^16*Defer[Int][1/(x*(-6 - 2*x^2 + x^3 + 9*Log[x] + 3*x^2*Log[x])), x] - 27*E^16*Defer[Int][Log[x^2]/(x*(-6
- 2*x^2 + x^3 + 9*Log[x] + 3*x^2*Log[x])^2), x] + 3*E^16*Defer[Int][(x*Log[x^2])/(-6 - 2*x^2 + x^3 + 9*Log[x]
+ 3*x^2*Log[x])^2, x] - 9*E^16*Defer[Int][(x^2*Log[x^2])/(-6 - 2*x^2 + x^3 + 9*Log[x] + 3*x^2*Log[x])^2, x] -
18*E^16*Defer[Int][(x*Log[x]*Log[x^2])/(-6 - 2*x^2 + x^3 + 9*Log[x] + 3*x^2*Log[x])^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 e^{16} \left (-12-4 x^2+2 x^3-\left (9-x^2+3 x^3\right ) \log \left (x^2\right )-6 \log (x) \left (-3-x^2+x^2 \log \left (x^2\right )\right )\right )}{x \left (6+2 x^2-x^3-3 \left (3+x^2\right ) \log (x)\right )^2} \, dx\\ &=\left (3 e^{16}\right ) \int \frac {-12-4 x^2+2 x^3-\left (9-x^2+3 x^3\right ) \log \left (x^2\right )-6 \log (x) \left (-3-x^2+x^2 \log \left (x^2\right )\right )}{x \left (6+2 x^2-x^3-3 \left (3+x^2\right ) \log (x)\right )^2} \, dx\\ &=\left (3 e^{16}\right ) \int \left (-\frac {12}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2}-\frac {4 x}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2}+\frac {2 x^2}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2}+\frac {18 \log (x)}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2}+\frac {6 x \log (x)}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2}-\frac {\left (9-x^2+3 x^3+6 x^2 \log (x)\right ) \log \left (x^2\right )}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2}\right ) \, dx\\ &=-\left (\left (3 e^{16}\right ) \int \frac {\left (9-x^2+3 x^3+6 x^2 \log (x)\right ) \log \left (x^2\right )}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx\right )+\left (6 e^{16}\right ) \int \frac {x^2}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx-\left (12 e^{16}\right ) \int \frac {x}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx+\left (18 e^{16}\right ) \int \frac {x \log (x)}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx-\left (36 e^{16}\right ) \int \frac {1}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx+\left (54 e^{16}\right ) \int \frac {\log (x)}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx\\ &=-\left (\left (3 e^{16}\right ) \int \left (\frac {9 \log \left (x^2\right )}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2}-\frac {x \log \left (x^2\right )}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2}+\frac {3 x^2 \log \left (x^2\right )}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2}+\frac {6 x \log (x) \log \left (x^2\right )}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2}\right ) \, dx\right )+\left (6 e^{16}\right ) \int \frac {x^2}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx-\left (12 e^{16}\right ) \int \frac {x}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx+\left (18 e^{16}\right ) \int \left (\frac {x \left (6+2 x^2-x^3\right )}{3 \left (3+x^2\right ) \left (6+2 x^2-x^3-9 \log (x)-3 x^2 \log (x)\right )^2}+\frac {x}{3 \left (3+x^2\right ) \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )}\right ) \, dx-\left (36 e^{16}\right ) \int \frac {1}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx+\left (54 e^{16}\right ) \int \left (\frac {6+2 x^2-x^3}{3 x \left (3+x^2\right ) \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2}+\frac {1}{3 x \left (3+x^2\right ) \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )}\right ) \, dx\\ &=\left (3 e^{16}\right ) \int \frac {x \log \left (x^2\right )}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx+\left (6 e^{16}\right ) \int \frac {x \left (6+2 x^2-x^3\right )}{\left (3+x^2\right ) \left (6+2 x^2-x^3-9 \log (x)-3 x^2 \log (x)\right )^2} \, dx+\left (6 e^{16}\right ) \int \frac {x^2}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx+\left (6 e^{16}\right ) \int \frac {x}{\left (3+x^2\right ) \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )} \, dx-\left (9 e^{16}\right ) \int \frac {x^2 \log \left (x^2\right )}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx-\left (12 e^{16}\right ) \int \frac {x}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx+\left (18 e^{16}\right ) \int \frac {6+2 x^2-x^3}{x \left (3+x^2\right ) \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx+\left (18 e^{16}\right ) \int \frac {1}{x \left (3+x^2\right ) \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )} \, dx-\left (18 e^{16}\right ) \int \frac {x \log (x) \log \left (x^2\right )}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx-\left (27 e^{16}\right ) \int \frac {\log \left (x^2\right )}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx-\left (36 e^{16}\right ) \int \frac {1}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx\\ &=\left (3 e^{16}\right ) \int \frac {x \log \left (x^2\right )}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx+\left (6 e^{16}\right ) \int \frac {x^2}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx+\left (6 e^{16}\right ) \int \left (\frac {3}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2}+\frac {2 x}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2}-\frac {x^2}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2}-\frac {9}{\left (3+x^2\right ) \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2}\right ) \, dx+\left (6 e^{16}\right ) \int \left (-\frac {1}{2 \left (i \sqrt {3}-x\right ) \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )}+\frac {1}{2 \left (i \sqrt {3}+x\right ) \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )}\right ) \, dx-\left (9 e^{16}\right ) \int \frac {x^2 \log \left (x^2\right )}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx-\left (12 e^{16}\right ) \int \frac {x}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx+\left (18 e^{16}\right ) \int \left (-\frac {1}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2}+\frac {2}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2}+\frac {3}{\left (3+x^2\right ) \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2}\right ) \, dx+\left (18 e^{16}\right ) \int \left (\frac {1}{3 x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )}-\frac {x}{3 \left (3+x^2\right ) \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )}\right ) \, dx-\left (18 e^{16}\right ) \int \frac {x \log (x) \log \left (x^2\right )}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx-\left (27 e^{16}\right ) \int \frac {\log \left (x^2\right )}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx-\left (36 e^{16}\right ) \int \frac {1}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx\\ &=-\left (\left (3 e^{16}\right ) \int \frac {1}{\left (i \sqrt {3}-x\right ) \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )} \, dx\right )+\left (3 e^{16}\right ) \int \frac {1}{\left (i \sqrt {3}+x\right ) \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )} \, dx+\left (3 e^{16}\right ) \int \frac {x \log \left (x^2\right )}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx+\left (6 e^{16}\right ) \int \frac {1}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )} \, dx-\left (6 e^{16}\right ) \int \frac {x}{\left (3+x^2\right ) \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )} \, dx-\left (9 e^{16}\right ) \int \frac {x^2 \log \left (x^2\right )}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx-\left (18 e^{16}\right ) \int \frac {x \log (x) \log \left (x^2\right )}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx-\left (27 e^{16}\right ) \int \frac {\log \left (x^2\right )}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx\\ &=-\left (\left (3 e^{16}\right ) \int \frac {1}{\left (i \sqrt {3}-x\right ) \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )} \, dx\right )+\left (3 e^{16}\right ) \int \frac {1}{\left (i \sqrt {3}+x\right ) \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )} \, dx+\left (3 e^{16}\right ) \int \frac {x \log \left (x^2\right )}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx+\left (6 e^{16}\right ) \int \frac {1}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )} \, dx-\left (6 e^{16}\right ) \int \left (-\frac {1}{2 \left (i \sqrt {3}-x\right ) \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )}+\frac {1}{2 \left (i \sqrt {3}+x\right ) \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )}\right ) \, dx-\left (9 e^{16}\right ) \int \frac {x^2 \log \left (x^2\right )}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx-\left (18 e^{16}\right ) \int \frac {x \log (x) \log \left (x^2\right )}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx-\left (27 e^{16}\right ) \int \frac {\log \left (x^2\right )}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx\\ &=\left (3 e^{16}\right ) \int \frac {x \log \left (x^2\right )}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx+\left (6 e^{16}\right ) \int \frac {1}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )} \, dx-\left (9 e^{16}\right ) \int \frac {x^2 \log \left (x^2\right )}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx-\left (18 e^{16}\right ) \int \frac {x \log (x) \log \left (x^2\right )}{\left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx-\left (27 e^{16}\right ) \int \frac {\log \left (x^2\right )}{x \left (-6-2 x^2+x^3+9 \log (x)+3 x^2 \log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.76, size = 30, normalized size = 1.00 \begin {gather*} \frac {3 e^{16} \log \left (x^2\right )}{-6-2 x^2+x^3+3 \left (3+x^2\right ) \log (x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^16*(-36 - 12*x^2 + 6*x^3) + E^16*(54 + 18*x^2)*Log[x] + (E^16*(-27 + 3*x^2 - 9*x^3) - 18*E^16*x^2
*Log[x])*Log[x^2])/(36*x + 24*x^3 - 12*x^4 + 4*x^5 - 4*x^6 + x^7 + (-108*x - 72*x^3 + 18*x^4 - 12*x^5 + 6*x^6)
*Log[x] + (81*x + 54*x^3 + 9*x^5)*Log[x]^2),x]

[Out]

(3*E^16*Log[x^2])/(-6 - 2*x^2 + x^3 + 3*(3 + x^2)*Log[x])

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fricas [A]  time = 1.05, size = 27, normalized size = 0.90 \begin {gather*} \frac {6 \, e^{16} \log \relax (x)}{x^{3} - 2 \, x^{2} + 3 \, {\left (x^{2} + 3\right )} \log \relax (x) - 6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-18*x^2*exp(16)*log(x)+(-9*x^3+3*x^2-27)*exp(16))*log(x^2)+(18*x^2+54)*exp(16)*log(x)+(6*x^3-12*x^
2-36)*exp(16))/((9*x^5+54*x^3+81*x)*log(x)^2+(6*x^6-12*x^5+18*x^4-72*x^3-108*x)*log(x)+x^7-4*x^6+4*x^5-12*x^4+
24*x^3+36*x),x, algorithm="fricas")

[Out]

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

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giac [A]  time = 0.32, size = 29, normalized size = 0.97 \begin {gather*} \frac {6 \, e^{16} \log \relax (x)}{x^{3} + 3 \, x^{2} \log \relax (x) - 2 \, x^{2} + 9 \, \log \relax (x) - 6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-18*x^2*exp(16)*log(x)+(-9*x^3+3*x^2-27)*exp(16))*log(x^2)+(18*x^2+54)*exp(16)*log(x)+(6*x^3-12*x^
2-36)*exp(16))/((9*x^5+54*x^3+81*x)*log(x)^2+(6*x^6-12*x^5+18*x^4-72*x^3-108*x)*log(x)+x^7-4*x^6+4*x^5-12*x^4+
24*x^3+36*x),x, algorithm="giac")

[Out]

6*e^16*log(x)/(x^3 + 3*x^2*log(x) - 2*x^2 + 9*log(x) - 6)

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maple [C]  time = 0.13, size = 166, normalized size = 5.53

method	result	size
risch	\(\frac {2 \,{\mathrm e}^{16}}{x^{2}+3}-\frac {\left (3 i \pi \,x^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-6 i \pi \,x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+3 i \pi \,x^{2} \mathrm {csgn}\left (i x^{2}\right )^{3}+9 i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x \right )^{2}-18 i \pi \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )+9 i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+4 x^{3}-8 x^{2}-24\right ) {\mathrm e}^{16}}{2 \left (x^{2}+3\right ) \left (3 x^{2} \ln \relax (x )+x^{3}-2 x^{2}+9 \ln \relax (x )-6\right )}\)	\(166\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-18*x^2*exp(16)*ln(x)+(-9*x^3+3*x^2-27)*exp(16))*ln(x^2)+(18*x^2+54)*exp(16)*ln(x)+(6*x^3-12*x^2-36)*exp
(16))/((9*x^5+54*x^3+81*x)*ln(x)^2+(6*x^6-12*x^5+18*x^4-72*x^3-108*x)*ln(x)+x^7-4*x^6+4*x^5-12*x^4+24*x^3+36*x
),x,method=_RETURNVERBOSE)

[Out]

2*exp(16)/(x^2+3)-1/2*(3*I*Pi*x^2*csgn(I*x)^2*csgn(I*x^2)-6*I*Pi*x^2*csgn(I*x)*csgn(I*x^2)^2+3*I*Pi*x^2*csgn(I
*x^2)^3+9*I*Pi*csgn(I*x)^2*csgn(I*x^2)-18*I*Pi*csgn(I*x)*csgn(I*x^2)^2+9*I*Pi*csgn(I*x^2)^3+4*x^3-8*x^2-24)*ex
p(16)/(x^2+3)/(3*x^2*ln(x)+x^3-2*x^2+9*ln(x)-6)

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maxima [A]  time = 0.56, size = 27, normalized size = 0.90 \begin {gather*} \frac {6 \, e^{16} \log \relax (x)}{x^{3} - 2 \, x^{2} + 3 \, {\left (x^{2} + 3\right )} \log \relax (x) - 6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-18*x^2*exp(16)*log(x)+(-9*x^3+3*x^2-27)*exp(16))*log(x^2)+(18*x^2+54)*exp(16)*log(x)+(6*x^3-12*x^
2-36)*exp(16))/((9*x^5+54*x^3+81*x)*log(x)^2+(6*x^6-12*x^5+18*x^4-72*x^3-108*x)*log(x)+x^7-4*x^6+4*x^5-12*x^4+
24*x^3+36*x),x, algorithm="maxima")

[Out]

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

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {\ln \left (x^2\right )\,\left ({\mathrm {e}}^{16}\,\left (9\,x^3-3\,x^2+27\right )+18\,x^2\,{\mathrm {e}}^{16}\,\ln \relax (x)\right )+{\mathrm {e}}^{16}\,\left (-6\,x^3+12\,x^2+36\right )-{\mathrm {e}}^{16}\,\ln \relax (x)\,\left (18\,x^2+54\right )}{36\,x+{\ln \relax (x)}^2\,\left (9\,x^5+54\,x^3+81\,x\right )-\ln \relax (x)\,\left (-6\,x^6+12\,x^5-18\,x^4+72\,x^3+108\,x\right )+24\,x^3-12\,x^4+4\,x^5-4\,x^6+x^7} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x^2)*(exp(16)*(9*x^3 - 3*x^2 + 27) + 18*x^2*exp(16)*log(x)) + exp(16)*(12*x^2 - 6*x^3 + 36) - exp(16
)*log(x)*(18*x^2 + 54))/(36*x + log(x)^2*(81*x + 54*x^3 + 9*x^5) - log(x)*(108*x + 72*x^3 - 18*x^4 + 12*x^5 -
6*x^6) + 24*x^3 - 12*x^4 + 4*x^5 - 4*x^6 + x^7),x)

[Out]

int(-(log(x^2)*(exp(16)*(9*x^3 - 3*x^2 + 27) + 18*x^2*exp(16)*log(x)) + exp(16)*(12*x^2 - 6*x^3 + 36) - exp(16
)*log(x)*(18*x^2 + 54))/(36*x + log(x)^2*(81*x + 54*x^3 + 9*x^5) - log(x)*(108*x + 72*x^3 - 18*x^4 + 12*x^5 -
6*x^6) + 24*x^3 - 12*x^4 + 4*x^5 - 4*x^6 + x^7), x)

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sympy [B]  time = 0.50, size = 68, normalized size = 2.27 \begin {gather*} \frac {- 2 x^{3} e^{16} + 4 x^{2} e^{16} + 12 e^{16}}{x^{5} - 2 x^{4} + 3 x^{3} - 12 x^{2} + \left (3 x^{4} + 18 x^{2} + 27\right ) \log {\relax (x )} - 18} + \frac {4 e^{16}}{2 x^{2} + 6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-18*x**2*exp(16)*ln(x)+(-9*x**3+3*x**2-27)*exp(16))*ln(x**2)+(18*x**2+54)*exp(16)*ln(x)+(6*x**3-12
*x**2-36)*exp(16))/((9*x**5+54*x**3+81*x)*ln(x)**2+(6*x**6-12*x**5+18*x**4-72*x**3-108*x)*ln(x)+x**7-4*x**6+4*
x**5-12*x**4+24*x**3+36*x),x)

[Out]

(-2*x**3*exp(16) + 4*x**2*exp(16) + 12*exp(16))/(x**5 - 2*x**4 + 3*x**3 - 12*x**2 + (3*x**4 + 18*x**2 + 27)*lo
g(x) - 18) + 4*exp(16)/(2*x**2 + 6)

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