3.51.85 \(\int \frac {e^{2/3} (-48 x^4-2 x^6)+\sqrt [3]{e} (-16800 x^4-480 x^5-700 x^6-20 x^7)+(e^{2/3} (-8 x^3+24 x^4)+\sqrt [3]{e} (-8560 x^3+8320 x^4)) \log (x^2)+(4 e^{2/3} x^3+\sqrt [3]{e} (-1440 x^2+4280 x^3+20 x^4)) \log ^2(x^2)+\sqrt [3]{e} (-80 x+720 x^2) \log ^3(x^2)+40 \sqrt [3]{e} x \log ^4(x^2)}{42875 x^6+3675 x^7+105 x^8+x^9+(44100 x^5+2520 x^6+36 x^7) \log (x^2)+(18795 x^4+642 x^5+3 x^6) \log ^2(x^2)+(4248 x^3+72 x^4) \log ^3(x^2)+(537 x^2+3 x^3) \log ^4(x^2)+36 x \log ^5(x^2)+\log ^6(x^2)} \, dx\)

Optimal. Leaf size=27 \[ \left (10+\frac {\sqrt [3]{e}}{-1+x+\left (6+\frac {\log \left (x^2\right )}{x}\right )^2}\right )^2 \]

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Rubi [F]  time = 3.21, 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^{2/3} \left (-48 x^4-2 x^6\right )+\sqrt [3]{e} \left (-16800 x^4-480 x^5-700 x^6-20 x^7\right )+\left (e^{2/3} \left (-8 x^3+24 x^4\right )+\sqrt [3]{e} \left (-8560 x^3+8320 x^4\right )\right ) \log \left (x^2\right )+\left (4 e^{2/3} x^3+\sqrt [3]{e} \left (-1440 x^2+4280 x^3+20 x^4\right )\right ) \log ^2\left (x^2\right )+\sqrt [3]{e} \left (-80 x+720 x^2\right ) \log ^3\left (x^2\right )+40 \sqrt [3]{e} x \log ^4\left (x^2\right )}{42875 x^6+3675 x^7+105 x^8+x^9+\left (44100 x^5+2520 x^6+36 x^7\right ) \log \left (x^2\right )+\left (18795 x^4+642 x^5+3 x^6\right ) \log ^2\left (x^2\right )+\left (4248 x^3+72 x^4\right ) \log ^3\left (x^2\right )+\left (537 x^2+3 x^3\right ) \log ^4\left (x^2\right )+36 x \log ^5\left (x^2\right )+\log ^6\left (x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(2/3)*(-48*x^4 - 2*x^6) + E^(1/3)*(-16800*x^4 - 480*x^5 - 700*x^6 - 20*x^7) + (E^(2/3)*(-8*x^3 + 24*x^4
) + E^(1/3)*(-8560*x^3 + 8320*x^4))*Log[x^2] + (4*E^(2/3)*x^3 + E^(1/3)*(-1440*x^2 + 4280*x^3 + 20*x^4))*Log[x
^2]^2 + E^(1/3)*(-80*x + 720*x^2)*Log[x^2]^3 + 40*E^(1/3)*x*Log[x^2]^4)/(42875*x^6 + 3675*x^7 + 105*x^8 + x^9
+ (44100*x^5 + 2520*x^6 + 36*x^7)*Log[x^2] + (18795*x^4 + 642*x^5 + 3*x^6)*Log[x^2]^2 + (4248*x^3 + 72*x^4)*Lo
g[x^2]^3 + (537*x^2 + 3*x^3)*Log[x^2]^4 + 36*x*Log[x^2]^5 + Log[x^2]^6),x]

[Out]

-48*E^(2/3)*Defer[Int][x^4/(35*x^2 + x^3 + 12*x*Log[x^2] + Log[x^2]^2)^3, x] - 140*E^(2/3)*Defer[Int][x^5/(35*
x^2 + x^3 + 12*x*Log[x^2] + Log[x^2]^2)^3, x] - 6*E^(2/3)*Defer[Int][x^6/(35*x^2 + x^3 + 12*x*Log[x^2] + Log[x
^2]^2)^3, x] - 8*E^(2/3)*Defer[Int][(x^3*Log[x^2])/(35*x^2 + x^3 + 12*x*Log[x^2] + Log[x^2]^2)^3, x] - 24*E^(2
/3)*Defer[Int][(x^4*Log[x^2])/(35*x^2 + x^3 + 12*x*Log[x^2] + Log[x^2]^2)^3, x] - 480*E^(1/3)*Defer[Int][x^2/(
35*x^2 + x^3 + 12*x*Log[x^2] + Log[x^2]^2)^2, x] - 4*(350 - E^(1/3))*E^(1/3)*Defer[Int][x^3/(35*x^2 + x^3 + 12
*x*Log[x^2] + Log[x^2]^2)^2, x] - 60*E^(1/3)*Defer[Int][x^4/(35*x^2 + x^3 + 12*x*Log[x^2] + Log[x^2]^2)^2, x]
- 80*E^(1/3)*Defer[Int][(x*Log[x^2])/(35*x^2 + x^3 + 12*x*Log[x^2] + Log[x^2]^2)^2, x] - 240*E^(1/3)*Defer[Int
][(x^2*Log[x^2])/(35*x^2 + x^3 + 12*x*Log[x^2] + Log[x^2]^2)^2, x] + 40*E^(1/3)*Defer[Int][x/(35*x^2 + x^3 + 1
2*x*Log[x^2] + Log[x^2]^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \sqrt [3]{e} x \left (-x^2 \left (\sqrt [3]{e}+10 (35+x)\right )-120 x \log \left (x^2\right )-10 \log ^2\left (x^2\right )\right ) \left (x \left (24+x^2\right )+(4-12 x) \log \left (x^2\right )-2 \log ^2\left (x^2\right )\right )}{\left (x^2 (35+x)+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3} \, dx\\ &=\left (2 \sqrt [3]{e}\right ) \int \frac {x \left (-x^2 \left (\sqrt [3]{e}+10 (35+x)\right )-120 x \log \left (x^2\right )-10 \log ^2\left (x^2\right )\right ) \left (x \left (24+x^2\right )+(4-12 x) \log \left (x^2\right )-2 \log ^2\left (x^2\right )\right )}{\left (x^2 (35+x)+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3} \, dx\\ &=\left (2 \sqrt [3]{e}\right ) \int \left (-\frac {\sqrt [3]{e} x^3 \left (24 x+70 x^2+3 x^3+4 \log \left (x^2\right )+12 x \log \left (x^2\right )\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3}+\frac {2 x \left (-120 x-350 \left (1-\frac {\sqrt [3]{e}}{350}\right ) x^2-15 x^3-20 \log \left (x^2\right )-60 x \log \left (x^2\right )\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2}+\frac {20 x}{35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )}\right ) \, dx\\ &=\left (4 \sqrt [3]{e}\right ) \int \frac {x \left (-120 x-350 \left (1-\frac {\sqrt [3]{e}}{350}\right ) x^2-15 x^3-20 \log \left (x^2\right )-60 x \log \left (x^2\right )\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2} \, dx+\left (40 \sqrt [3]{e}\right ) \int \frac {x}{35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx-\left (2 e^{2/3}\right ) \int \frac {x^3 \left (24 x+70 x^2+3 x^3+4 \log \left (x^2\right )+12 x \log \left (x^2\right )\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3} \, dx\\ &=\left (4 \sqrt [3]{e}\right ) \int \left (-\frac {120 x^2}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2}+\frac {\left (-350+\sqrt [3]{e}\right ) x^3}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2}-\frac {15 x^4}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2}-\frac {20 x \log \left (x^2\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2}-\frac {60 x^2 \log \left (x^2\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2}\right ) \, dx+\left (40 \sqrt [3]{e}\right ) \int \frac {x}{35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx-\left (2 e^{2/3}\right ) \int \left (\frac {24 x^4}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3}+\frac {70 x^5}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3}+\frac {3 x^6}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3}+\frac {4 x^3 \log \left (x^2\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3}+\frac {12 x^4 \log \left (x^2\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3}\right ) \, dx\\ &=\left (40 \sqrt [3]{e}\right ) \int \frac {x}{35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx-\left (60 \sqrt [3]{e}\right ) \int \frac {x^4}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2} \, dx-\left (80 \sqrt [3]{e}\right ) \int \frac {x \log \left (x^2\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2} \, dx-\left (240 \sqrt [3]{e}\right ) \int \frac {x^2 \log \left (x^2\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2} \, dx-\left (480 \sqrt [3]{e}\right ) \int \frac {x^2}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2} \, dx-\left (4 \left (350-\sqrt [3]{e}\right ) \sqrt [3]{e}\right ) \int \frac {x^3}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2} \, dx-\left (6 e^{2/3}\right ) \int \frac {x^6}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3} \, dx-\left (8 e^{2/3}\right ) \int \frac {x^3 \log \left (x^2\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3} \, dx-\left (24 e^{2/3}\right ) \int \frac {x^4 \log \left (x^2\right )}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3} \, dx-\left (48 e^{2/3}\right ) \int \frac {x^4}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3} \, dx-\left (140 e^{2/3}\right ) \int \frac {x^5}{\left (35 x^2+x^3+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^3} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.09, size = 63, normalized size = 2.33 \begin {gather*} \frac {\sqrt [3]{e} x^2 \left (x^2 \left (\sqrt [3]{e}+20 (35+x)\right )+240 x \log \left (x^2\right )+20 \log ^2\left (x^2\right )\right )}{\left (x^2 (35+x)+12 x \log \left (x^2\right )+\log ^2\left (x^2\right )\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(2/3)*(-48*x^4 - 2*x^6) + E^(1/3)*(-16800*x^4 - 480*x^5 - 700*x^6 - 20*x^7) + (E^(2/3)*(-8*x^3 +
24*x^4) + E^(1/3)*(-8560*x^3 + 8320*x^4))*Log[x^2] + (4*E^(2/3)*x^3 + E^(1/3)*(-1440*x^2 + 4280*x^3 + 20*x^4))
*Log[x^2]^2 + E^(1/3)*(-80*x + 720*x^2)*Log[x^2]^3 + 40*E^(1/3)*x*Log[x^2]^4)/(42875*x^6 + 3675*x^7 + 105*x^8
+ x^9 + (44100*x^5 + 2520*x^6 + 36*x^7)*Log[x^2] + (18795*x^4 + 642*x^5 + 3*x^6)*Log[x^2]^2 + (4248*x^3 + 72*x
^4)*Log[x^2]^3 + (537*x^2 + 3*x^3)*Log[x^2]^4 + 36*x*Log[x^2]^5 + Log[x^2]^6),x]

[Out]

(E^(1/3)*x^2*(x^2*(E^(1/3) + 20*(35 + x)) + 240*x*Log[x^2] + 20*Log[x^2]^2))/(x^2*(35 + x) + 12*x*Log[x^2] + L
og[x^2]^2)^2

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fricas [B]  time = 0.87, size = 108, normalized size = 4.00 \begin {gather*} \frac {x^{4} e^{\frac {2}{3}} + 240 \, x^{3} e^{\frac {1}{3}} \log \left (x^{2}\right ) + 20 \, x^{2} e^{\frac {1}{3}} \log \left (x^{2}\right )^{2} + 20 \, {\left (x^{5} + 35 \, x^{4}\right )} e^{\frac {1}{3}}}{x^{6} + 70 \, x^{5} + 1225 \, x^{4} + 24 \, x \log \left (x^{2}\right )^{3} + \log \left (x^{2}\right )^{4} + 2 \, {\left (x^{3} + 107 \, x^{2}\right )} \log \left (x^{2}\right )^{2} + 24 \, {\left (x^{4} + 35 \, x^{3}\right )} \log \left (x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((40*x*exp(1/3)*log(x^2)^4+(720*x^2-80*x)*exp(1/3)*log(x^2)^3+(4*x^3*exp(1/3)^2+(20*x^4+4280*x^3-1440
*x^2)*exp(1/3))*log(x^2)^2+((24*x^4-8*x^3)*exp(1/3)^2+(8320*x^4-8560*x^3)*exp(1/3))*log(x^2)+(-2*x^6-48*x^4)*e
xp(1/3)^2+(-20*x^7-700*x^6-480*x^5-16800*x^4)*exp(1/3))/(log(x^2)^6+36*x*log(x^2)^5+(3*x^3+537*x^2)*log(x^2)^4
+(72*x^4+4248*x^3)*log(x^2)^3+(3*x^6+642*x^5+18795*x^4)*log(x^2)^2+(36*x^7+2520*x^6+44100*x^5)*log(x^2)+x^9+10
5*x^8+3675*x^7+42875*x^6),x, algorithm="fricas")

[Out]

(x^4*e^(2/3) + 240*x^3*e^(1/3)*log(x^2) + 20*x^2*e^(1/3)*log(x^2)^2 + 20*(x^5 + 35*x^4)*e^(1/3))/(x^6 + 70*x^5
+ 1225*x^4 + 24*x*log(x^2)^3 + log(x^2)^4 + 2*(x^3 + 107*x^2)*log(x^2)^2 + 24*(x^4 + 35*x^3)*log(x^2))

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giac [B]  time = 0.72, size = 117, normalized size = 4.33 \begin {gather*} \frac {20 \, x^{5} e^{\frac {1}{3}} + x^{4} e^{\frac {2}{3}} + 700 \, x^{4} e^{\frac {1}{3}} + 240 \, x^{3} e^{\frac {1}{3}} \log \left (x^{2}\right ) + 20 \, x^{2} e^{\frac {1}{3}} \log \left (x^{2}\right )^{2}}{x^{6} + 70 \, x^{5} + 24 \, x^{4} \log \left (x^{2}\right ) + 2 \, x^{3} \log \left (x^{2}\right )^{2} + 1225 \, x^{4} + 840 \, x^{3} \log \left (x^{2}\right ) + 214 \, x^{2} \log \left (x^{2}\right )^{2} + 24 \, x \log \left (x^{2}\right )^{3} + \log \left (x^{2}\right )^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((40*x*exp(1/3)*log(x^2)^4+(720*x^2-80*x)*exp(1/3)*log(x^2)^3+(4*x^3*exp(1/3)^2+(20*x^4+4280*x^3-1440
*x^2)*exp(1/3))*log(x^2)^2+((24*x^4-8*x^3)*exp(1/3)^2+(8320*x^4-8560*x^3)*exp(1/3))*log(x^2)+(-2*x^6-48*x^4)*e
xp(1/3)^2+(-20*x^7-700*x^6-480*x^5-16800*x^4)*exp(1/3))/(log(x^2)^6+36*x*log(x^2)^5+(3*x^3+537*x^2)*log(x^2)^4
+(72*x^4+4248*x^3)*log(x^2)^3+(3*x^6+642*x^5+18795*x^4)*log(x^2)^2+(36*x^7+2520*x^6+44100*x^5)*log(x^2)+x^9+10
5*x^8+3675*x^7+42875*x^6),x, algorithm="giac")

[Out]

(20*x^5*e^(1/3) + x^4*e^(2/3) + 700*x^4*e^(1/3) + 240*x^3*e^(1/3)*log(x^2) + 20*x^2*e^(1/3)*log(x^2)^2)/(x^6 +
70*x^5 + 24*x^4*log(x^2) + 2*x^3*log(x^2)^2 + 1225*x^4 + 840*x^3*log(x^2) + 214*x^2*log(x^2)^2 + 24*x*log(x^2
)^3 + log(x^2)^4)

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maple [B]  time = 0.06, size = 63, normalized size = 2.33

method	result	size
risch	\(\frac {\left (x^{2} {\mathrm e}^{\frac {1}{3}}+20 x^{3}+700 x^{2}+240 x \ln \left (x^{2}\right )+20 \ln \left (x^{2}\right )^{2}\right ) x^{2} {\mathrm e}^{\frac {1}{3}}}{\left (x^{3}+\ln \left (x^{2}\right )^{2}+12 x \ln \left (x^{2}\right )+35 x^{2}\right )^{2}}\)	\(63\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((40*x*exp(1/3)*ln(x^2)^4+(720*x^2-80*x)*exp(1/3)*ln(x^2)^3+(4*x^3*exp(1/3)^2+(20*x^4+4280*x^3-1440*x^2)*ex
p(1/3))*ln(x^2)^2+((24*x^4-8*x^3)*exp(1/3)^2+(8320*x^4-8560*x^3)*exp(1/3))*ln(x^2)+(-2*x^6-48*x^4)*exp(1/3)^2+
(-20*x^7-700*x^6-480*x^5-16800*x^4)*exp(1/3))/(ln(x^2)^6+36*x*ln(x^2)^5+(3*x^3+537*x^2)*ln(x^2)^4+(72*x^4+4248
*x^3)*ln(x^2)^3+(3*x^6+642*x^5+18795*x^4)*ln(x^2)^2+(36*x^7+2520*x^6+44100*x^5)*ln(x^2)+x^9+105*x^8+3675*x^7+4
2875*x^6),x,method=_RETURNVERBOSE)

[Out]

(x^2*exp(1/3)+20*x^3+700*x^2+240*x*ln(x^2)+20*ln(x^2)^2)*x^2*exp(1/3)/(x^3+ln(x^2)^2+12*x*ln(x^2)+35*x^2)^2

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maxima [B]  time = 5.43, size = 97, normalized size = 3.59 \begin {gather*} \frac {20 \, x^{5} e^{\frac {1}{3}} + x^{4} {\left (e^{\frac {2}{3}} + 700 \, e^{\frac {1}{3}}\right )} + 480 \, x^{3} e^{\frac {1}{3}} \log \relax (x) + 80 \, x^{2} e^{\frac {1}{3}} \log \relax (x)^{2}}{x^{6} + 70 \, x^{5} + 1225 \, x^{4} + 192 \, x \log \relax (x)^{3} + 16 \, \log \relax (x)^{4} + 8 \, {\left (x^{3} + 107 \, x^{2}\right )} \log \relax (x)^{2} + 48 \, {\left (x^{4} + 35 \, x^{3}\right )} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((40*x*exp(1/3)*log(x^2)^4+(720*x^2-80*x)*exp(1/3)*log(x^2)^3+(4*x^3*exp(1/3)^2+(20*x^4+4280*x^3-1440
*x^2)*exp(1/3))*log(x^2)^2+((24*x^4-8*x^3)*exp(1/3)^2+(8320*x^4-8560*x^3)*exp(1/3))*log(x^2)+(-2*x^6-48*x^4)*e
xp(1/3)^2+(-20*x^7-700*x^6-480*x^5-16800*x^4)*exp(1/3))/(log(x^2)^6+36*x*log(x^2)^5+(3*x^3+537*x^2)*log(x^2)^4
+(72*x^4+4248*x^3)*log(x^2)^3+(3*x^6+642*x^5+18795*x^4)*log(x^2)^2+(36*x^7+2520*x^6+44100*x^5)*log(x^2)+x^9+10
5*x^8+3675*x^7+42875*x^6),x, algorithm="maxima")

[Out]

(20*x^5*e^(1/3) + x^4*(e^(2/3) + 700*e^(1/3)) + 480*x^3*e^(1/3)*log(x) + 80*x^2*e^(1/3)*log(x)^2)/(x^6 + 70*x^
5 + 1225*x^4 + 192*x*log(x)^3 + 16*log(x)^4 + 8*(x^3 + 107*x^2)*log(x)^2 + 48*(x^4 + 35*x^3)*log(x))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {-40\,x\,{\mathrm {e}}^{1/3}\,{\ln \left (x^2\right )}^4+{\mathrm {e}}^{1/3}\,\left (80\,x-720\,x^2\right )\,{\ln \left (x^2\right )}^3+\left (-4\,x^3\,{\mathrm {e}}^{2/3}-{\mathrm {e}}^{1/3}\,\left (20\,x^4+4280\,x^3-1440\,x^2\right )\right )\,{\ln \left (x^2\right )}^2+\left ({\mathrm {e}}^{2/3}\,\left (8\,x^3-24\,x^4\right )+{\mathrm {e}}^{1/3}\,\left (8560\,x^3-8320\,x^4\right )\right )\,\ln \left (x^2\right )+{\mathrm {e}}^{2/3}\,\left (2\,x^6+48\,x^4\right )+{\mathrm {e}}^{1/3}\,\left (20\,x^7+700\,x^6+480\,x^5+16800\,x^4\right )}{{\ln \left (x^2\right )}^2\,\left (3\,x^6+642\,x^5+18795\,x^4\right )+36\,x\,{\ln \left (x^2\right )}^5+{\ln \left (x^2\right )}^6+\ln \left (x^2\right )\,\left (36\,x^7+2520\,x^6+44100\,x^5\right )+{\ln \left (x^2\right )}^4\,\left (3\,x^3+537\,x^2\right )+{\ln \left (x^2\right )}^3\,\left (72\,x^4+4248\,x^3\right )+42875\,x^6+3675\,x^7+105\,x^8+x^9} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x^2)*(exp(2/3)*(8*x^3 - 24*x^4) + exp(1/3)*(8560*x^3 - 8320*x^4)) + exp(2/3)*(48*x^4 + 2*x^6) - log(
x^2)^2*(4*x^3*exp(2/3) + exp(1/3)*(4280*x^3 - 1440*x^2 + 20*x^4)) + exp(1/3)*(16800*x^4 + 480*x^5 + 700*x^6 +
20*x^7) + log(x^2)^3*exp(1/3)*(80*x - 720*x^2) - 40*x*log(x^2)^4*exp(1/3))/(log(x^2)^2*(18795*x^4 + 642*x^5 +
3*x^6) + 36*x*log(x^2)^5 + log(x^2)^6 + log(x^2)*(44100*x^5 + 2520*x^6 + 36*x^7) + log(x^2)^4*(537*x^2 + 3*x^3
) + log(x^2)^3*(4248*x^3 + 72*x^4) + 42875*x^6 + 3675*x^7 + 105*x^8 + x^9),x)

[Out]

int(-(log(x^2)*(exp(2/3)*(8*x^3 - 24*x^4) + exp(1/3)*(8560*x^3 - 8320*x^4)) + exp(2/3)*(48*x^4 + 2*x^6) - log(
x^2)^2*(4*x^3*exp(2/3) + exp(1/3)*(4280*x^3 - 1440*x^2 + 20*x^4)) + exp(1/3)*(16800*x^4 + 480*x^5 + 700*x^6 +
20*x^7) + log(x^2)^3*exp(1/3)*(80*x - 720*x^2) - 40*x*log(x^2)^4*exp(1/3))/(log(x^2)^2*(18795*x^4 + 642*x^5 +
3*x^6) + 36*x*log(x^2)^5 + log(x^2)^6 + log(x^2)*(44100*x^5 + 2520*x^6 + 36*x^7) + log(x^2)^4*(537*x^2 + 3*x^3
) + log(x^2)^3*(4248*x^3 + 72*x^4) + 42875*x^6 + 3675*x^7 + 105*x^8 + x^9), x)

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sympy [B]  time = 0.31, size = 122, normalized size = 4.52 \begin {gather*} \frac {20 x^{5} e^{\frac {1}{3}} + x^{4} e^{\frac {2}{3}} + 700 x^{4} e^{\frac {1}{3}} + 240 x^{3} e^{\frac {1}{3}} \log {\left (x^{2} \right )} + 20 x^{2} e^{\frac {1}{3}} \log {\left (x^{2} \right )}^{2}}{x^{6} + 70 x^{5} + 1225 x^{4} + 24 x \log {\left (x^{2} \right )}^{3} + \left (2 x^{3} + 214 x^{2}\right ) \log {\left (x^{2} \right )}^{2} + \left (24 x^{4} + 840 x^{3}\right ) \log {\left (x^{2} \right )} + \log {\left (x^{2} \right )}^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((40*x*exp(1/3)*ln(x**2)**4+(720*x**2-80*x)*exp(1/3)*ln(x**2)**3+(4*x**3*exp(1/3)**2+(20*x**4+4280*x*
*3-1440*x**2)*exp(1/3))*ln(x**2)**2+((24*x**4-8*x**3)*exp(1/3)**2+(8320*x**4-8560*x**3)*exp(1/3))*ln(x**2)+(-2
*x**6-48*x**4)*exp(1/3)**2+(-20*x**7-700*x**6-480*x**5-16800*x**4)*exp(1/3))/(ln(x**2)**6+36*x*ln(x**2)**5+(3*
x**3+537*x**2)*ln(x**2)**4+(72*x**4+4248*x**3)*ln(x**2)**3+(3*x**6+642*x**5+18795*x**4)*ln(x**2)**2+(36*x**7+2
520*x**6+44100*x**5)*ln(x**2)+x**9+105*x**8+3675*x**7+42875*x**6),x)

[Out]

(20*x**5*exp(1/3) + x**4*exp(2/3) + 700*x**4*exp(1/3) + 240*x**3*exp(1/3)*log(x**2) + 20*x**2*exp(1/3)*log(x**
2)**2)/(x**6 + 70*x**5 + 1225*x**4 + 24*x*log(x**2)**3 + (2*x**3 + 214*x**2)*log(x**2)**2 + (24*x**4 + 840*x**
3)*log(x**2) + log(x**2)**4)

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