3.5.46 \(\int \frac {90 x^2+90 x \log (3)+(x+\log (3))^{\frac {2 x^2}{5}} (2 x^2+(4 x^2+4 x \log (3)) \log (x+\log (3)))+(x+\log (3))^{\frac {x^2}{5}} (-30 x-6 x^3-30 \log (3)+(-12 x^3-12 x^2 \log (3)) \log (x+\log (3)))}{5 x+5 \log (3)} \, dx\)

Optimal. Leaf size=20 \[ \left (3 x-(x+\log (3))^{\frac {x^2}{5}}\right )^2 \]

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Rubi [F]  time = 0.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(90*x^2 + 90*x*Log[3] + (x + Log[3])^((2*x^2)/5)*(2*x^2 + (4*x^2 + 4*x*Log[3])*Log[x + Log[3]]) + (x + Log
[3])^(x^2/5)*(-30*x - 6*x^3 - 30*Log[3] + (-12*x^3 - 12*x^2*Log[3])*Log[x + Log[3]]))/(5*x + 5*Log[3]),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [F]  time = 0.51, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {90 x^2+90 x \log (3)+(x+\log (3))^{\frac {2 x^2}{5}} \left (2 x^2+\left (4 x^2+4 x \log (3)\right ) \log (x+\log (3))\right )+(x+\log (3))^{\frac {x^2}{5}} \left (-30 x-6 x^3-30 \log (3)+\left (-12 x^3-12 x^2 \log (3)\right ) \log (x+\log (3))\right )}{5 x+5 \log (3)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(90*x^2 + 90*x*Log[3] + (x + Log[3])^((2*x^2)/5)*(2*x^2 + (4*x^2 + 4*x*Log[3])*Log[x + Log[3]]) + (x
+ Log[3])^(x^2/5)*(-30*x - 6*x^3 - 30*Log[3] + (-12*x^3 - 12*x^2*Log[3])*Log[x + Log[3]]))/(5*x + 5*Log[3]),x
]

[Out]

Integrate[(90*x^2 + 90*x*Log[3] + (x + Log[3])^((2*x^2)/5)*(2*x^2 + (4*x^2 + 4*x*Log[3])*Log[x + Log[3]]) + (x
+ Log[3])^(x^2/5)*(-30*x - 6*x^3 - 30*Log[3] + (-12*x^3 - 12*x^2*Log[3])*Log[x + Log[3]]))/(5*x + 5*Log[3]),
x]

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fricas [A]  time = 0.93, size = 29, normalized size = 1.45 \begin {gather*} -6 \, {\left (x + \log \relax (3)\right )}^{\frac {1}{5} \, x^{2}} x + 9 \, x^{2} + {\left (x + \log \relax (3)\right )}^{\frac {2}{5} \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x*log(3)+4*x^2)*log(log(3)+x)+2*x^2)*exp(1/5*x^2*log(log(3)+x))^2+((-12*x^2*log(3)-12*x^3)*log(
log(3)+x)-30*log(3)-6*x^3-30*x)*exp(1/5*x^2*log(log(3)+x))+90*x*log(3)+90*x^2)/(5*log(3)+5*x),x, algorithm="fr
icas")

[Out]

-6*(x + log(3))^(1/5*x^2)*x + 9*x^2 + (x + log(3))^(2/5*x^2)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, {\left ({\left (x^{2} + 2 \, {\left (x^{2} + x \log \relax (3)\right )} \log \left (x + \log \relax (3)\right )\right )} {\left (x + \log \relax (3)\right )}^{\frac {2}{5} \, x^{2}} - 3 \, {\left (x^{3} + 2 \, {\left (x^{3} + x^{2} \log \relax (3)\right )} \log \left (x + \log \relax (3)\right ) + 5 \, x + 5 \, \log \relax (3)\right )} {\left (x + \log \relax (3)\right )}^{\frac {1}{5} \, x^{2}} + 45 \, x^{2} + 45 \, x \log \relax (3)\right )}}{5 \, {\left (x + \log \relax (3)\right )}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x*log(3)+4*x^2)*log(log(3)+x)+2*x^2)*exp(1/5*x^2*log(log(3)+x))^2+((-12*x^2*log(3)-12*x^3)*log(
log(3)+x)-30*log(3)-6*x^3-30*x)*exp(1/5*x^2*log(log(3)+x))+90*x*log(3)+90*x^2)/(5*log(3)+5*x),x, algorithm="gi
ac")

[Out]

integrate(2/5*((x^2 + 2*(x^2 + x*log(3))*log(x + log(3)))*(x + log(3))^(2/5*x^2) - 3*(x^3 + 2*(x^3 + x^2*log(3
))*log(x + log(3)) + 5*x + 5*log(3))*(x + log(3))^(1/5*x^2) + 45*x^2 + 45*x*log(3))/(x + log(3)), x)

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maple [A]  time = 0.36, size = 32, normalized size = 1.60

method	result	size
risch	\(\left (\ln \relax (3)+x \right )^{\frac {2 x^{2}}{5}}-6 x \left (\ln \relax (3)+x \right )^{\frac {x^{2}}{5}}+9 x^{2}\)	\(32\)
default	\({\mathrm e}^{x^{2} \ln \left (\left (\ln \relax (3)+x \right )^{\frac {2}{5}}\right )}-6 x \,{\mathrm e}^{\frac {x^{2} \ln \left (\ln \relax (3)+x \right )}{5}}+9 x^{2}\)	\(34\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((4*x*ln(3)+4*x^2)*ln(ln(3)+x)+2*x^2)*exp(1/5*x^2*ln(ln(3)+x))^2+((-12*x^2*ln(3)-12*x^3)*ln(ln(3)+x)-30*l
n(3)-6*x^3-30*x)*exp(1/5*x^2*ln(ln(3)+x))+90*x*ln(3)+90*x^2)/(5*ln(3)+5*x),x,method=_RETURNVERBOSE)

[Out]

((ln(3)+x)^(1/5*x^2))^2-6*x*(ln(3)+x)^(1/5*x^2)+9*x^2

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maxima [B]  time = 0.60, size = 61, normalized size = 3.05 \begin {gather*} 18 \, \log \relax (3)^{2} \log \left (x + \log \relax (3)\right ) - 6 \, {\left (x + \log \relax (3)\right )}^{\frac {1}{5} \, x^{2}} x + 9 \, x^{2} - 18 \, {\left (\log \relax (3) \log \left (x + \log \relax (3)\right ) - x\right )} \log \relax (3) - 18 \, x \log \relax (3) + {\left (x + \log \relax (3)\right )}^{\frac {2}{5} \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x*log(3)+4*x^2)*log(log(3)+x)+2*x^2)*exp(1/5*x^2*log(log(3)+x))^2+((-12*x^2*log(3)-12*x^3)*log(
log(3)+x)-30*log(3)-6*x^3-30*x)*exp(1/5*x^2*log(log(3)+x))+90*x*log(3)+90*x^2)/(5*log(3)+5*x),x, algorithm="ma
xima")

[Out]

18*log(3)^2*log(x + log(3)) - 6*(x + log(3))^(1/5*x^2)*x + 9*x^2 - 18*(log(3)*log(x + log(3)) - x)*log(3) - 18
*x*log(3) + (x + log(3))^(2/5*x^2)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {{\mathrm {e}}^{\frac {2\,x^2\,\ln \left (x+\ln \relax (3)\right )}{5}}\,\left (2\,x^2+\ln \left (x+\ln \relax (3)\right )\,\left (4\,x^2+4\,\ln \relax (3)\,x\right )\right )-{\mathrm {e}}^{\frac {x^2\,\ln \left (x+\ln \relax (3)\right )}{5}}\,\left (30\,x+30\,\ln \relax (3)+\ln \left (x+\ln \relax (3)\right )\,\left (12\,x^3+12\,\ln \relax (3)\,x^2\right )+6\,x^3\right )+90\,x\,\ln \relax (3)+90\,x^2}{5\,x+5\,\ln \relax (3)} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((2*x^2*log(x + log(3)))/5)*(2*x^2 + log(x + log(3))*(4*x*log(3) + 4*x^2)) - exp((x^2*log(x + log(3)))
/5)*(30*x + 30*log(3) + log(x + log(3))*(12*x^2*log(3) + 12*x^3) + 6*x^3) + 90*x*log(3) + 90*x^2)/(5*x + 5*log
(3)),x)

[Out]

int((exp((2*x^2*log(x + log(3)))/5)*(2*x^2 + log(x + log(3))*(4*x*log(3) + 4*x^2)) - exp((x^2*log(x + log(3)))
/5)*(30*x + 30*log(3) + log(x + log(3))*(12*x^2*log(3) + 12*x^3) + 6*x^3) + 90*x*log(3) + 90*x^2)/(5*x + 5*log
(3)), x)

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sympy [B]  time = 0.54, size = 36, normalized size = 1.80 \begin {gather*} 9 x^{2} - 6 x e^{\frac {x^{2} \log {\left (x + \log {\relax (3 )} \right )}}{5}} + e^{\frac {2 x^{2} \log {\left (x + \log {\relax (3 )} \right )}}{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x*ln(3)+4*x**2)*ln(ln(3)+x)+2*x**2)*exp(1/5*x**2*ln(ln(3)+x))**2+((-12*x**2*ln(3)-12*x**3)*ln(l
n(3)+x)-30*ln(3)-6*x**3-30*x)*exp(1/5*x**2*ln(ln(3)+x))+90*x*ln(3)+90*x**2)/(5*ln(3)+5*x),x)

[Out]

9*x**2 - 6*x*exp(x**2*log(x + log(3))/5) + exp(2*x**2*log(x + log(3))/5)

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