3.61.10 \(\int \frac {(-15+x^2) \log (x^2)+(180+24 x-12 x^2) \log (\log (x^2))+(-45-3 x^2) \log (x^2) \log ^2(\log (x^2))}{(225-240 x+94 x^2-16 x^3+x^4) \log (x^2)+(1350-540 x-96 x^2+60 x^3-6 x^4) \log (x^2) \log ^2(\log (x^2))+(2025+540 x-234 x^2-36 x^3+9 x^4) \log (x^2) \log ^4(\log (x^2))} \, dx\)

Optimal. Leaf size=26 \[ \frac {x}{(-5+x) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )} \]

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Rubi [F]  time = 9.63, 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 {\left (-15+x^2\right ) \log \left (x^2\right )+\left (180+24 x-12 x^2\right ) \log \left (\log \left (x^2\right )\right )+\left (-45-3 x^2\right ) \log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )}{\left (225-240 x+94 x^2-16 x^3+x^4\right ) \log \left (x^2\right )+\left (1350-540 x-96 x^2+60 x^3-6 x^4\right ) \log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )+\left (2025+540 x-234 x^2-36 x^3+9 x^4\right ) \log \left (x^2\right ) \log ^4\left (\log \left (x^2\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((-15 + x^2)*Log[x^2] + (180 + 24*x - 12*x^2)*Log[Log[x^2]] + (-45 - 3*x^2)*Log[x^2]*Log[Log[x^2]]^2)/((22
5 - 240*x + 94*x^2 - 16*x^3 + x^4)*Log[x^2] + (1350 - 540*x - 96*x^2 + 60*x^3 - 6*x^4)*Log[x^2]*Log[Log[x^2]]^
2 + (2025 + 540*x - 234*x^2 - 36*x^3 + 9*x^4)*Log[x^2]*Log[Log[x^2]]^4),x]

[Out]

-5*Defer[Int][1/((-5 + x)^2*(3 - x + 9*Log[Log[x^2]]^2 + 3*x*Log[Log[x^2]]^2)), x] + (15*Defer[Int][1/((-5 + x
)*(3 - x + 3*(3 + x)*Log[Log[x^2]]^2)^2), x])/4 + (9*Defer[Int][1/((3 + x)*(3 - x + 3*(3 + x)*Log[Log[x^2]]^2)
^2), x])/4 - 12*Defer[Int][Log[Log[x^2]]/(Log[x^2]*(3 - x + 3*(3 + x)*Log[Log[x^2]]^2)^2), x] - 96*Defer[Int][
Log[Log[x^2]]/((-5 + x)*Log[x^2]*(3 - x + 3*(3 + x)*Log[Log[x^2]]^2)^2), x] - (5*Defer[Int][1/((-5 + x)*(3 - x
+ 3*(3 + x)*Log[Log[x^2]]^2)), x])/8 - (3*Defer[Int][1/((3 + x)*(3 - x + 3*(3 + x)*Log[Log[x^2]]^2)), x])/8

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-12 \left (-15-2 x+x^2\right ) \log \left (\log \left (x^2\right )\right )+\log \left (x^2\right ) \left (-15+x^2-3 \left (15+x^2\right ) \log ^2\left (\log \left (x^2\right )\right )\right )}{\log \left (x^2\right ) \left (15-8 x+x^2+\left (45+6 x-3 x^2\right ) \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx\\ &=\int \left (-\frac {6 \left (-x \log \left (x^2\right )+18 \log \left (\log \left (x^2\right )\right )+12 x \log \left (\log \left (x^2\right )\right )+2 x^2 \log \left (\log \left (x^2\right )\right )\right )}{(-5+x) (3+x) \log \left (x^2\right ) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2}+\frac {-15-x^2}{(-5+x)^2 (3+x) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )}\right ) \, dx\\ &=-\left (6 \int \frac {-x \log \left (x^2\right )+18 \log \left (\log \left (x^2\right )\right )+12 x \log \left (\log \left (x^2\right )\right )+2 x^2 \log \left (\log \left (x^2\right )\right )}{(-5+x) (3+x) \log \left (x^2\right ) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx\right )+\int \frac {-15-x^2}{(-5+x)^2 (3+x) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx\\ &=-\left (6 \int \frac {x \log \left (x^2\right )-2 (3+x)^2 \log \left (\log \left (x^2\right )\right )}{(5-x) (3+x) \log \left (x^2\right ) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx\right )+\int \left (-\frac {5}{(-5+x)^2 \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )}-\frac {5}{8 (-5+x) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )}-\frac {3}{8 (3+x) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )}\right ) \, dx\\ &=-\left (\frac {3}{8} \int \frac {1}{(3+x) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx\right )-\frac {5}{8} \int \frac {1}{(-5+x) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx-5 \int \frac {1}{(-5+x)^2 \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx-6 \int \left (\frac {x \log \left (x^2\right )-18 \log \left (\log \left (x^2\right )\right )-12 x \log \left (\log \left (x^2\right )\right )-2 x^2 \log \left (\log \left (x^2\right )\right )}{8 (3+x) \log \left (x^2\right ) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2}+\frac {-x \log \left (x^2\right )+18 \log \left (\log \left (x^2\right )\right )+12 x \log \left (\log \left (x^2\right )\right )+2 x^2 \log \left (\log \left (x^2\right )\right )}{8 (-5+x) \log \left (x^2\right ) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2}\right ) \, dx\\ &=-\left (\frac {3}{8} \int \frac {1}{(3+x) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx\right )-\frac {5}{8} \int \frac {1}{(-5+x) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx-\frac {3}{4} \int \frac {x \log \left (x^2\right )-18 \log \left (\log \left (x^2\right )\right )-12 x \log \left (\log \left (x^2\right )\right )-2 x^2 \log \left (\log \left (x^2\right )\right )}{(3+x) \log \left (x^2\right ) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx-\frac {3}{4} \int \frac {-x \log \left (x^2\right )+18 \log \left (\log \left (x^2\right )\right )+12 x \log \left (\log \left (x^2\right )\right )+2 x^2 \log \left (\log \left (x^2\right )\right )}{(-5+x) \log \left (x^2\right ) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx-5 \int \frac {1}{(-5+x)^2 \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx\\ &=-\left (\frac {3}{8} \int \frac {1}{(3+x) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx\right )-\frac {5}{8} \int \frac {1}{(-5+x) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx-\frac {3}{4} \int \frac {x \log \left (x^2\right )-2 (3+x)^2 \log \left (\log \left (x^2\right )\right )}{(5-x) \log \left (x^2\right ) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx-\frac {3}{4} \int \frac {x \log \left (x^2\right )-2 (3+x)^2 \log \left (\log \left (x^2\right )\right )}{(3+x) \log \left (x^2\right ) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx-5 \int \frac {1}{(-5+x)^2 \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx\\ &=-\left (\frac {3}{8} \int \frac {1}{(3+x) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx\right )-\frac {5}{8} \int \frac {1}{(-5+x) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx-\frac {3}{4} \int \left (-\frac {x}{(-5+x) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2}+\frac {18 \log \left (\log \left (x^2\right )\right )}{(-5+x) \log \left (x^2\right ) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2}+\frac {12 x \log \left (\log \left (x^2\right )\right )}{(-5+x) \log \left (x^2\right ) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2}+\frac {2 x^2 \log \left (\log \left (x^2\right )\right )}{(-5+x) \log \left (x^2\right ) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2}\right ) \, dx-\frac {3}{4} \int \left (\frac {x}{(3+x) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2}-\frac {18 \log \left (\log \left (x^2\right )\right )}{(3+x) \log \left (x^2\right ) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2}-\frac {12 x \log \left (\log \left (x^2\right )\right )}{(3+x) \log \left (x^2\right ) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2}-\frac {2 x^2 \log \left (\log \left (x^2\right )\right )}{(3+x) \log \left (x^2\right ) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2}\right ) \, dx-5 \int \frac {1}{(-5+x)^2 \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx\\ &=-\left (\frac {3}{8} \int \frac {1}{(3+x) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx\right )-\frac {5}{8} \int \frac {1}{(-5+x) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx+\frac {3}{4} \int \frac {x}{(-5+x) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx-\frac {3}{4} \int \frac {x}{(3+x) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx-\frac {3}{2} \int \frac {x^2 \log \left (\log \left (x^2\right )\right )}{(-5+x) \log \left (x^2\right ) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx+\frac {3}{2} \int \frac {x^2 \log \left (\log \left (x^2\right )\right )}{(3+x) \log \left (x^2\right ) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx-5 \int \frac {1}{(-5+x)^2 \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx-9 \int \frac {x \log \left (\log \left (x^2\right )\right )}{(-5+x) \log \left (x^2\right ) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx+9 \int \frac {x \log \left (\log \left (x^2\right )\right )}{(3+x) \log \left (x^2\right ) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx-\frac {27}{2} \int \frac {\log \left (\log \left (x^2\right )\right )}{(-5+x) \log \left (x^2\right ) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx+\frac {27}{2} \int \frac {\log \left (\log \left (x^2\right )\right )}{(3+x) \log \left (x^2\right ) \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx\\ &=-\left (\frac {3}{8} \int \frac {1}{(3+x) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx\right )-\frac {5}{8} \int \frac {1}{(-5+x) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx+\frac {3}{4} \int \frac {x}{(-5+x) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx-\frac {3}{4} \int \frac {x}{(3+x) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx-\frac {3}{2} \int \frac {x^2 \log \left (\log \left (x^2\right )\right )}{(-5+x) \log \left (x^2\right ) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx+\frac {3}{2} \int \frac {x^2 \log \left (\log \left (x^2\right )\right )}{(3+x) \log \left (x^2\right ) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx-5 \int \frac {1}{(-5+x)^2 \left (3-x+9 \log ^2\left (\log \left (x^2\right )\right )+3 x \log ^2\left (\log \left (x^2\right )\right )\right )} \, dx-9 \int \frac {x \log \left (\log \left (x^2\right )\right )}{(-5+x) \log \left (x^2\right ) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx+9 \int \frac {x \log \left (\log \left (x^2\right )\right )}{(3+x) \log \left (x^2\right ) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx-\frac {27}{2} \int \frac {\log \left (\log \left (x^2\right )\right )}{(-5+x) \log \left (x^2\right ) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx+\frac {27}{2} \int \frac {\log \left (\log \left (x^2\right )\right )}{(3+x) \log \left (x^2\right ) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.55, size = 26, normalized size = 1.00 \begin {gather*} \frac {x}{(-5+x) \left (3-x+3 (3+x) \log ^2\left (\log \left (x^2\right )\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((-15 + x^2)*Log[x^2] + (180 + 24*x - 12*x^2)*Log[Log[x^2]] + (-45 - 3*x^2)*Log[x^2]*Log[Log[x^2]]^2
)/((225 - 240*x + 94*x^2 - 16*x^3 + x^4)*Log[x^2] + (1350 - 540*x - 96*x^2 + 60*x^3 - 6*x^4)*Log[x^2]*Log[Log[
x^2]]^2 + (2025 + 540*x - 234*x^2 - 36*x^3 + 9*x^4)*Log[x^2]*Log[Log[x^2]]^4),x]

[Out]

x/((-5 + x)*(3 - x + 3*(3 + x)*Log[Log[x^2]]^2))

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fricas [A]  time = 0.81, size = 31, normalized size = 1.19 \begin {gather*} \frac {x}{3 \, {\left (x^{2} - 2 \, x - 15\right )} \log \left (\log \left (x^{2}\right )\right )^{2} - x^{2} + 8 \, x - 15} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3*x^2-45)*log(x^2)*log(log(x^2))^2+(-12*x^2+24*x+180)*log(log(x^2))+(x^2-15)*log(x^2))/((9*x^4-36
*x^3-234*x^2+540*x+2025)*log(x^2)*log(log(x^2))^4+(-6*x^4+60*x^3-96*x^2-540*x+1350)*log(x^2)*log(log(x^2))^2+(
x^4-16*x^3+94*x^2-240*x+225)*log(x^2)),x, algorithm="fricas")

[Out]

x/(3*(x^2 - 2*x - 15)*log(log(x^2))^2 - x^2 + 8*x - 15)

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giac [A]  time = 1.61, size = 45, normalized size = 1.73 \begin {gather*} \frac {x}{3 \, x^{2} \log \left (\log \left (x^{2}\right )\right )^{2} - 6 \, x \log \left (\log \left (x^{2}\right )\right )^{2} - x^{2} - 45 \, \log \left (\log \left (x^{2}\right )\right )^{2} + 8 \, x - 15} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3*x^2-45)*log(x^2)*log(log(x^2))^2+(-12*x^2+24*x+180)*log(log(x^2))+(x^2-15)*log(x^2))/((9*x^4-36
*x^3-234*x^2+540*x+2025)*log(x^2)*log(log(x^2))^4+(-6*x^4+60*x^3-96*x^2-540*x+1350)*log(x^2)*log(log(x^2))^2+(
x^4-16*x^3+94*x^2-240*x+225)*log(x^2)),x, algorithm="giac")

[Out]

x/(3*x^2*log(log(x^2))^2 - 6*x*log(log(x^2))^2 - x^2 - 45*log(log(x^2))^2 + 8*x - 15)

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maple [F]  time = 0.03, size = 0, normalized size = 0.00 \[\int \frac {\left (-3 x^{2}-45\right ) \ln \left (x^{2}\right ) \ln \left (\ln \left (x^{2}\right )\right )^{2}+\left (-12 x^{2}+24 x +180\right ) \ln \left (\ln \left (x^{2}\right )\right )+\left (x^{2}-15\right ) \ln \left (x^{2}\right )}{\left (9 x^{4}-36 x^{3}-234 x^{2}+540 x +2025\right ) \ln \left (x^{2}\right ) \ln \left (\ln \left (x^{2}\right )\right )^{4}+\left (-6 x^{4}+60 x^{3}-96 x^{2}-540 x +1350\right ) \ln \left (x^{2}\right ) \ln \left (\ln \left (x^{2}\right )\right )^{2}+\left (x^{4}-16 x^{3}+94 x^{2}-240 x +225\right ) \ln \left (x^{2}\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-3*x^2-45)*ln(x^2)*ln(ln(x^2))^2+(-12*x^2+24*x+180)*ln(ln(x^2))+(x^2-15)*ln(x^2))/((9*x^4-36*x^3-234*x^2
+540*x+2025)*ln(x^2)*ln(ln(x^2))^4+(-6*x^4+60*x^3-96*x^2-540*x+1350)*ln(x^2)*ln(ln(x^2))^2+(x^4-16*x^3+94*x^2-
240*x+225)*ln(x^2)),x)

[Out]

int(((-3*x^2-45)*ln(x^2)*ln(ln(x^2))^2+(-12*x^2+24*x+180)*ln(ln(x^2))+(x^2-15)*ln(x^2))/((9*x^4-36*x^3-234*x^2
+540*x+2025)*ln(x^2)*ln(ln(x^2))^4+(-6*x^4+60*x^3-96*x^2-540*x+1350)*ln(x^2)*ln(ln(x^2))^2+(x^4-16*x^3+94*x^2-
240*x+225)*ln(x^2)),x)

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maxima [B]  time = 0.53, size = 71, normalized size = 2.73 \begin {gather*} \frac {x}{{\left (3 \, \log \relax (2)^{2} - 1\right )} x^{2} + 3 \, {\left (x^{2} - 2 \, x - 15\right )} \log \left (\log \relax (x)\right )^{2} - 2 \, {\left (3 \, \log \relax (2)^{2} - 4\right )} x - 45 \, \log \relax (2)^{2} + 6 \, {\left (x^{2} \log \relax (2) - 2 \, x \log \relax (2) - 15 \, \log \relax (2)\right )} \log \left (\log \relax (x)\right ) - 15} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3*x^2-45)*log(x^2)*log(log(x^2))^2+(-12*x^2+24*x+180)*log(log(x^2))+(x^2-15)*log(x^2))/((9*x^4-36
*x^3-234*x^2+540*x+2025)*log(x^2)*log(log(x^2))^4+(-6*x^4+60*x^3-96*x^2-540*x+1350)*log(x^2)*log(log(x^2))^2+(
x^4-16*x^3+94*x^2-240*x+225)*log(x^2)),x, algorithm="maxima")

[Out]

x/((3*log(2)^2 - 1)*x^2 + 3*(x^2 - 2*x - 15)*log(log(x))^2 - 2*(3*log(2)^2 - 4)*x - 45*log(2)^2 + 6*(x^2*log(2
) - 2*x*log(2) - 15*log(2))*log(log(x)) - 15)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {-\ln \left (x^2\right )\,\left (3\,x^2+45\right )\,{\ln \left (\ln \left (x^2\right )\right )}^2+\left (-12\,x^2+24\,x+180\right )\,\ln \left (\ln \left (x^2\right )\right )+\ln \left (x^2\right )\,\left (x^2-15\right )}{\ln \left (x^2\right )\,\left (9\,x^4-36\,x^3-234\,x^2+540\,x+2025\right )\,{\ln \left (\ln \left (x^2\right )\right )}^4-\ln \left (x^2\right )\,\left (6\,x^4-60\,x^3+96\,x^2+540\,x-1350\right )\,{\ln \left (\ln \left (x^2\right )\right )}^2+\ln \left (x^2\right )\,\left (x^4-16\,x^3+94\,x^2-240\,x+225\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(log(x^2))*(24*x - 12*x^2 + 180) + log(x^2)*(x^2 - 15) - log(x^2)*log(log(x^2))^2*(3*x^2 + 45))/(log(x
^2)*(94*x^2 - 240*x - 16*x^3 + x^4 + 225) - log(x^2)*log(log(x^2))^2*(540*x + 96*x^2 - 60*x^3 + 6*x^4 - 1350)
+ log(x^2)*log(log(x^2))^4*(540*x - 234*x^2 - 36*x^3 + 9*x^4 + 2025)),x)

[Out]

int((log(log(x^2))*(24*x - 12*x^2 + 180) + log(x^2)*(x^2 - 15) - log(x^2)*log(log(x^2))^2*(3*x^2 + 45))/(log(x
^2)*(94*x^2 - 240*x - 16*x^3 + x^4 + 225) - log(x^2)*log(log(x^2))^2*(540*x + 96*x^2 - 60*x^3 + 6*x^4 - 1350)
+ log(x^2)*log(log(x^2))^4*(540*x - 234*x^2 - 36*x^3 + 9*x^4 + 2025)), x)

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sympy [A]  time = 0.44, size = 27, normalized size = 1.04 \begin {gather*} \frac {x}{- x^{2} + 8 x + \left (3 x^{2} - 6 x - 45\right ) \log {\left (\log {\left (x^{2} \right )} \right )}^{2} - 15} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3*x**2-45)*ln(x**2)*ln(ln(x**2))**2+(-12*x**2+24*x+180)*ln(ln(x**2))+(x**2-15)*ln(x**2))/((9*x**4
-36*x**3-234*x**2+540*x+2025)*ln(x**2)*ln(ln(x**2))**4+(-6*x**4+60*x**3-96*x**2-540*x+1350)*ln(x**2)*ln(ln(x**
2))**2+(x**4-16*x**3+94*x**2-240*x+225)*ln(x**2)),x)

[Out]

x/(-x**2 + 8*x + (3*x**2 - 6*x - 45)*log(log(x**2))**2 - 15)

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