3.100.58 \(\int \frac {-18 x^2-6 x^3+e^2 (-18 x-6 x^2)+e^2 (-18 x-6 x^2) \log (x)-15 x \log ^2(x)+(90+30 x) \log ^2(x) \log (3+x)+e^{e^x} (-3 x \log ^2(x)+(18+6 x+e^x (-9 x-3 x^2)) \log ^2(x) \log (3+x))}{(3 x^3+x^4) \log ^2(x)} \, dx\)

Optimal. Leaf size=33 \[ \frac {3 \left (\frac {2 \left (e^2+x\right )}{\log (x)}-\frac {\left (5+e^{e^x}\right ) \log (3+x)}{x}\right )}{x} \]

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Rubi [F]  time = 6.23, 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 {-18 x^2-6 x^3+e^2 \left (-18 x-6 x^2\right )+e^2 \left (-18 x-6 x^2\right ) \log (x)-15 x \log ^2(x)+(90+30 x) \log ^2(x) \log (3+x)+e^{e^x} \left (-3 x \log ^2(x)+\left (18+6 x+e^x \left (-9 x-3 x^2\right )\right ) \log ^2(x) \log (3+x)\right )}{\left (3 x^3+x^4\right ) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-18*x^2 - 6*x^3 + E^2*(-18*x - 6*x^2) + E^2*(-18*x - 6*x^2)*Log[x] - 15*x*Log[x]^2 + (90 + 30*x)*Log[x]^2
*Log[3 + x] + E^E^x*(-3*x*Log[x]^2 + (18 + 6*x + E^x*(-9*x - 3*x^2))*Log[x]^2*Log[3 + x]))/((3*x^3 + x^4)*Log[
x]^2),x]

[Out]

6/Log[x] + (6*E^2)/(x*Log[x]) - (15*Log[3 + x])/x^2 + 6*Log[3 + x]*Defer[Int][E^E^x/x^3, x] - Defer[Int][E^E^x
/x^2, x] - 3*Log[3 + x]*Defer[Int][E^(E^x + x)/x^2, x] + Defer[Int][E^E^x/x, x]/3 - Defer[Int][E^E^x/(3 + x),
x]/3 - 6*Defer[Int][Defer[Int][E^E^x/x^3, x]/(3 + x), x] + 3*Defer[Int][Defer[Int][E^(E^x + x)/x^2, x]/(3 + x)
, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-18 x^2-6 x^3+e^2 \left (-18 x-6 x^2\right )+e^2 \left (-18 x-6 x^2\right ) \log (x)-15 x \log ^2(x)+(90+30 x) \log ^2(x) \log (3+x)+e^{e^x} \left (-3 x \log ^2(x)+\left (18+6 x+e^x \left (-9 x-3 x^2\right )\right ) \log ^2(x) \log (3+x)\right )}{x^3 (3+x) \log ^2(x)} \, dx\\ &=\int \frac {3 \left (-2 x (3+x) \left (e^2+x\right )-2 e^2 x (3+x) \log (x)-\log ^2(x) \left (\left (5+e^{e^x}\right ) x+(3+x) \left (-10-2 e^{e^x}+e^{e^x+x} x\right ) \log (3+x)\right )\right )}{x^3 (3+x) \log ^2(x)} \, dx\\ &=3 \int \frac {-2 x (3+x) \left (e^2+x\right )-2 e^2 x (3+x) \log (x)-\log ^2(x) \left (\left (5+e^{e^x}\right ) x+(3+x) \left (-10-2 e^{e^x}+e^{e^x+x} x\right ) \log (3+x)\right )}{x^3 (3+x) \log ^2(x)} \, dx\\ &=3 \int \left (-\frac {e^{e^x+x} \log (3+x)}{x^2}+\frac {-6 e^2 x-6 \left (1+\frac {e^2}{3}\right ) x^2-2 x^3-6 e^2 x \log (x)-2 e^2 x^2 \log (x)-5 x \log ^2(x)-e^{e^x} x \log ^2(x)+30 \log ^2(x) \log (3+x)+6 e^{e^x} \log ^2(x) \log (3+x)+10 x \log ^2(x) \log (3+x)+2 e^{e^x} x \log ^2(x) \log (3+x)}{x^3 (3+x) \log ^2(x)}\right ) \, dx\\ &=-\left (3 \int \frac {e^{e^x+x} \log (3+x)}{x^2} \, dx\right )+3 \int \frac {-6 e^2 x-6 \left (1+\frac {e^2}{3}\right ) x^2-2 x^3-6 e^2 x \log (x)-2 e^2 x^2 \log (x)-5 x \log ^2(x)-e^{e^x} x \log ^2(x)+30 \log ^2(x) \log (3+x)+6 e^{e^x} \log ^2(x) \log (3+x)+10 x \log ^2(x) \log (3+x)+2 e^{e^x} x \log ^2(x) \log (3+x)}{x^3 (3+x) \log ^2(x)} \, dx\\ &=3 \int \frac {-\frac {2 x \left (e^2+x\right )}{\log ^2(x)}-\frac {2 e^2 x}{\log (x)}+\frac {\left (5+e^{e^x}\right ) (-x+2 (3+x) \log (3+x))}{3+x}}{x^3} \, dx+3 \int \frac {\int \frac {e^{e^x+x}}{x^2} \, dx}{3+x} \, dx-(3 \log (3+x)) \int \frac {e^{e^x+x}}{x^2} \, dx\\ &=3 \int \left (\frac {e^{e^x} (-x+6 \log (3+x)+2 x \log (3+x))}{x^3 (3+x)}+\frac {-6 e^2 x-6 \left (1+\frac {e^2}{3}\right ) x^2-2 x^3-6 e^2 x \log (x)-2 e^2 x^2 \log (x)-5 x \log ^2(x)+30 \log ^2(x) \log (3+x)+10 x \log ^2(x) \log (3+x)}{x^3 (3+x) \log ^2(x)}\right ) \, dx+3 \int \frac {\int \frac {e^{e^x+x}}{x^2} \, dx}{3+x} \, dx-(3 \log (3+x)) \int \frac {e^{e^x+x}}{x^2} \, dx\\ &=3 \int \frac {e^{e^x} (-x+6 \log (3+x)+2 x \log (3+x))}{x^3 (3+x)} \, dx+3 \int \frac {-6 e^2 x-6 \left (1+\frac {e^2}{3}\right ) x^2-2 x^3-6 e^2 x \log (x)-2 e^2 x^2 \log (x)-5 x \log ^2(x)+30 \log ^2(x) \log (3+x)+10 x \log ^2(x) \log (3+x)}{x^3 (3+x) \log ^2(x)} \, dx+3 \int \frac {\int \frac {e^{e^x+x}}{x^2} \, dx}{3+x} \, dx-(3 \log (3+x)) \int \frac {e^{e^x+x}}{x^2} \, dx\\ &=3 \int \frac {-\frac {5 x}{3+x}-\frac {2 x \left (e^2+x\right )}{\log ^2(x)}-\frac {2 e^2 x}{\log (x)}+10 \log (3+x)}{x^3} \, dx+3 \int \left (-\frac {e^{e^x}}{x^2 (3+x)}+\frac {2 e^{e^x} \log (3+x)}{x^3}\right ) \, dx+3 \int \frac {\int \frac {e^{e^x+x}}{x^2} \, dx}{3+x} \, dx-(3 \log (3+x)) \int \frac {e^{e^x+x}}{x^2} \, dx\\ &=-\left (3 \int \frac {e^{e^x}}{x^2 (3+x)} \, dx\right )+3 \int \left (\frac {-6 e^2-6 \left (1+\frac {e^2}{3}\right ) x-2 x^2-6 e^2 \log (x)-2 e^2 x \log (x)-5 \log ^2(x)}{x^2 (3+x) \log ^2(x)}+\frac {10 \log (3+x)}{x^3}\right ) \, dx+3 \int \frac {\int \frac {e^{e^x+x}}{x^2} \, dx}{3+x} \, dx+6 \int \frac {e^{e^x} \log (3+x)}{x^3} \, dx-(3 \log (3+x)) \int \frac {e^{e^x+x}}{x^2} \, dx\\ &=-\left (3 \int \left (\frac {e^{e^x}}{3 x^2}-\frac {e^{e^x}}{9 x}+\frac {e^{e^x}}{9 (3+x)}\right ) \, dx\right )+3 \int \frac {-6 e^2-6 \left (1+\frac {e^2}{3}\right ) x-2 x^2-6 e^2 \log (x)-2 e^2 x \log (x)-5 \log ^2(x)}{x^2 (3+x) \log ^2(x)} \, dx+3 \int \frac {\int \frac {e^{e^x+x}}{x^2} \, dx}{3+x} \, dx-6 \int \frac {\int \frac {e^{e^x}}{x^3} \, dx}{3+x} \, dx+30 \int \frac {\log (3+x)}{x^3} \, dx-(3 \log (3+x)) \int \frac {e^{e^x+x}}{x^2} \, dx+(6 \log (3+x)) \int \frac {e^{e^x}}{x^3} \, dx\\ &=-\frac {15 \log (3+x)}{x^2}+\frac {1}{3} \int \frac {e^{e^x}}{x} \, dx-\frac {1}{3} \int \frac {e^{e^x}}{3+x} \, dx+3 \int \frac {-2 (3+x) \left (e^2+x\right )-2 e^2 (3+x) \log (x)-5 \log ^2(x)}{x^2 (3+x) \log ^2(x)} \, dx+3 \int \frac {\int \frac {e^{e^x+x}}{x^2} \, dx}{3+x} \, dx-6 \int \frac {\int \frac {e^{e^x}}{x^3} \, dx}{3+x} \, dx+15 \int \frac {1}{x^2 (3+x)} \, dx-(3 \log (3+x)) \int \frac {e^{e^x+x}}{x^2} \, dx+(6 \log (3+x)) \int \frac {e^{e^x}}{x^3} \, dx-\int \frac {e^{e^x}}{x^2} \, dx\\ &=-\frac {15 \log (3+x)}{x^2}+\frac {1}{3} \int \frac {e^{e^x}}{x} \, dx-\frac {1}{3} \int \frac {e^{e^x}}{3+x} \, dx+3 \int \left (-\frac {5}{x^2 (3+x)}-\frac {2 \left (e^2+x\right )}{x^2 \log ^2(x)}-\frac {2 e^2}{x^2 \log (x)}\right ) \, dx+3 \int \frac {\int \frac {e^{e^x+x}}{x^2} \, dx}{3+x} \, dx-6 \int \frac {\int \frac {e^{e^x}}{x^3} \, dx}{3+x} \, dx+15 \int \left (\frac {1}{3 x^2}-\frac {1}{9 x}+\frac {1}{9 (3+x)}\right ) \, dx-(3 \log (3+x)) \int \frac {e^{e^x+x}}{x^2} \, dx+(6 \log (3+x)) \int \frac {e^{e^x}}{x^3} \, dx-\int \frac {e^{e^x}}{x^2} \, dx\\ &=-\frac {5}{x}-\frac {5 \log (x)}{3}+\frac {5}{3} \log (3+x)-\frac {15 \log (3+x)}{x^2}+\frac {1}{3} \int \frac {e^{e^x}}{x} \, dx-\frac {1}{3} \int \frac {e^{e^x}}{3+x} \, dx+3 \int \frac {\int \frac {e^{e^x+x}}{x^2} \, dx}{3+x} \, dx-6 \int \frac {e^2+x}{x^2 \log ^2(x)} \, dx-6 \int \frac {\int \frac {e^{e^x}}{x^3} \, dx}{3+x} \, dx-15 \int \frac {1}{x^2 (3+x)} \, dx-\left (6 e^2\right ) \int \frac {1}{x^2 \log (x)} \, dx-(3 \log (3+x)) \int \frac {e^{e^x+x}}{x^2} \, dx+(6 \log (3+x)) \int \frac {e^{e^x}}{x^3} \, dx-\int \frac {e^{e^x}}{x^2} \, dx\\ &=-\frac {5}{x}-\frac {5 \log (x)}{3}+\frac {5}{3} \log (3+x)-\frac {15 \log (3+x)}{x^2}+\frac {1}{3} \int \frac {e^{e^x}}{x} \, dx-\frac {1}{3} \int \frac {e^{e^x}}{3+x} \, dx+3 \int \frac {\int \frac {e^{e^x+x}}{x^2} \, dx}{3+x} \, dx-6 \int \left (\frac {e^2}{x^2 \log ^2(x)}+\frac {1}{x \log ^2(x)}\right ) \, dx-6 \int \frac {\int \frac {e^{e^x}}{x^3} \, dx}{3+x} \, dx-15 \int \left (\frac {1}{3 x^2}-\frac {1}{9 x}+\frac {1}{9 (3+x)}\right ) \, dx-\left (6 e^2\right ) \operatorname {Subst}\left (\int \frac {e^{-x}}{x} \, dx,x,\log (x)\right )-(3 \log (3+x)) \int \frac {e^{e^x+x}}{x^2} \, dx+(6 \log (3+x)) \int \frac {e^{e^x}}{x^3} \, dx-\int \frac {e^{e^x}}{x^2} \, dx\\ &=-6 e^2 \text {Ei}(-\log (x))-\frac {15 \log (3+x)}{x^2}+\frac {1}{3} \int \frac {e^{e^x}}{x} \, dx-\frac {1}{3} \int \frac {e^{e^x}}{3+x} \, dx+3 \int \frac {\int \frac {e^{e^x+x}}{x^2} \, dx}{3+x} \, dx-6 \int \frac {1}{x \log ^2(x)} \, dx-6 \int \frac {\int \frac {e^{e^x}}{x^3} \, dx}{3+x} \, dx-\left (6 e^2\right ) \int \frac {1}{x^2 \log ^2(x)} \, dx-(3 \log (3+x)) \int \frac {e^{e^x+x}}{x^2} \, dx+(6 \log (3+x)) \int \frac {e^{e^x}}{x^3} \, dx-\int \frac {e^{e^x}}{x^2} \, dx\\ &=-6 e^2 \text {Ei}(-\log (x))+\frac {6 e^2}{x \log (x)}-\frac {15 \log (3+x)}{x^2}+\frac {1}{3} \int \frac {e^{e^x}}{x} \, dx-\frac {1}{3} \int \frac {e^{e^x}}{3+x} \, dx+3 \int \frac {\int \frac {e^{e^x+x}}{x^2} \, dx}{3+x} \, dx-6 \int \frac {\int \frac {e^{e^x}}{x^3} \, dx}{3+x} \, dx-6 \operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log (x)\right )+\left (6 e^2\right ) \int \frac {1}{x^2 \log (x)} \, dx-(3 \log (3+x)) \int \frac {e^{e^x+x}}{x^2} \, dx+(6 \log (3+x)) \int \frac {e^{e^x}}{x^3} \, dx-\int \frac {e^{e^x}}{x^2} \, dx\\ &=-6 e^2 \text {Ei}(-\log (x))+\frac {6}{\log (x)}+\frac {6 e^2}{x \log (x)}-\frac {15 \log (3+x)}{x^2}+\frac {1}{3} \int \frac {e^{e^x}}{x} \, dx-\frac {1}{3} \int \frac {e^{e^x}}{3+x} \, dx+3 \int \frac {\int \frac {e^{e^x+x}}{x^2} \, dx}{3+x} \, dx-6 \int \frac {\int \frac {e^{e^x}}{x^3} \, dx}{3+x} \, dx+\left (6 e^2\right ) \operatorname {Subst}\left (\int \frac {e^{-x}}{x} \, dx,x,\log (x)\right )-(3 \log (3+x)) \int \frac {e^{e^x+x}}{x^2} \, dx+(6 \log (3+x)) \int \frac {e^{e^x}}{x^3} \, dx-\int \frac {e^{e^x}}{x^2} \, dx\\ &=\frac {6}{\log (x)}+\frac {6 e^2}{x \log (x)}-\frac {15 \log (3+x)}{x^2}+\frac {1}{3} \int \frac {e^{e^x}}{x} \, dx-\frac {1}{3} \int \frac {e^{e^x}}{3+x} \, dx+3 \int \frac {\int \frac {e^{e^x+x}}{x^2} \, dx}{3+x} \, dx-6 \int \frac {\int \frac {e^{e^x}}{x^3} \, dx}{3+x} \, dx-(3 \log (3+x)) \int \frac {e^{e^x+x}}{x^2} \, dx+(6 \log (3+x)) \int \frac {e^{e^x}}{x^3} \, dx-\int \frac {e^{e^x}}{x^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.69, size = 32, normalized size = 0.97 \begin {gather*} -\frac {3 \left (-2 x \left (e^2+x\right )+\left (5+e^{e^x}\right ) \log (x) \log (3+x)\right )}{x^2 \log (x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-18*x^2 - 6*x^3 + E^2*(-18*x - 6*x^2) + E^2*(-18*x - 6*x^2)*Log[x] - 15*x*Log[x]^2 + (90 + 30*x)*Lo
g[x]^2*Log[3 + x] + E^E^x*(-3*x*Log[x]^2 + (18 + 6*x + E^x*(-9*x - 3*x^2))*Log[x]^2*Log[3 + x]))/((3*x^3 + x^4
)*Log[x]^2),x]

[Out]

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

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fricas [A]  time = 0.69, size = 38, normalized size = 1.15 \begin {gather*} -\frac {3 \, {\left (e^{\left (e^{x}\right )} \log \left (x + 3\right ) \log \relax (x) - 2 \, x^{2} - 2 \, x e^{2} + 5 \, \log \left (x + 3\right ) \log \relax (x)\right )}}{x^{2} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-3*x^2-9*x)*exp(x)+18+6*x)*log(x)^2*log(3+x)-3*x*log(x)^2)*exp(exp(x))+(30*x+90)*log(x)^2*log(3+
x)-15*x*log(x)^2+(-6*x^2-18*x)*exp(2)*log(x)+(-6*x^2-18*x)*exp(2)-6*x^3-18*x^2)/(x^4+3*x^3)/log(x)^2,x, algori
thm="fricas")

[Out]

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

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {3 \, {\left (10 \, {\left (x + 3\right )} \log \left (x + 3\right ) \log \relax (x)^{2} - 2 \, x^{3} - 2 \, {\left (x^{2} + 3 \, x\right )} e^{2} \log \relax (x) - 5 \, x \log \relax (x)^{2} - 6 \, x^{2} - 2 \, {\left (x^{2} + 3 \, x\right )} e^{2} - {\left ({\left ({\left (x^{2} + 3 \, x\right )} e^{x} - 2 \, x - 6\right )} \log \left (x + 3\right ) \log \relax (x)^{2} + x \log \relax (x)^{2}\right )} e^{\left (e^{x}\right )}\right )}}{{\left (x^{4} + 3 \, x^{3}\right )} \log \relax (x)^{2}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-3*x^2-9*x)*exp(x)+18+6*x)*log(x)^2*log(3+x)-3*x*log(x)^2)*exp(exp(x))+(30*x+90)*log(x)^2*log(3+
x)-15*x*log(x)^2+(-6*x^2-18*x)*exp(2)*log(x)+(-6*x^2-18*x)*exp(2)-6*x^3-18*x^2)/(x^4+3*x^3)/log(x)^2,x, algori
thm="giac")

[Out]

integrate(3*(10*(x + 3)*log(x + 3)*log(x)^2 - 2*x^3 - 2*(x^2 + 3*x)*e^2*log(x) - 5*x*log(x)^2 - 6*x^2 - 2*(x^2
+ 3*x)*e^2 - (((x^2 + 3*x)*e^x - 2*x - 6)*log(x + 3)*log(x)^2 + x*log(x)^2)*e^(e^x))/((x^4 + 3*x^3)*log(x)^2)
, x)

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maple [A]  time = 0.12, size = 36, normalized size = 1.09

method	result	size
risch	\(-\frac {15 \ln \left (3+x \right )}{x^{2}}+\frac {6 x +6 \,{\mathrm e}^{2}}{x \ln \relax (x )}-\frac {3 \ln \left (3+x \right ) {\mathrm e}^{{\mathrm e}^{x}}}{x^{2}}\)	\(36\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((-3*x^2-9*x)*exp(x)+18+6*x)*ln(x)^2*ln(3+x)-3*x*ln(x)^2)*exp(exp(x))+(30*x+90)*ln(x)^2*ln(3+x)-15*x*ln(
x)^2+(-6*x^2-18*x)*exp(2)*ln(x)+(-6*x^2-18*x)*exp(2)-6*x^3-18*x^2)/(x^4+3*x^3)/ln(x)^2,x,method=_RETURNVERBOSE
)

[Out]

-15/x^2*ln(3+x)+6/x*(x+exp(2))/ln(x)-3/x^2*ln(3+x)*exp(exp(x))

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maxima [A]  time = 0.40, size = 38, normalized size = 1.15 \begin {gather*} -\frac {3 \, {\left (e^{\left (e^{x}\right )} \log \left (x + 3\right ) \log \relax (x) - 2 \, x^{2} - 2 \, x e^{2} + 5 \, \log \left (x + 3\right ) \log \relax (x)\right )}}{x^{2} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-3*x^2-9*x)*exp(x)+18+6*x)*log(x)^2*log(3+x)-3*x*log(x)^2)*exp(exp(x))+(30*x+90)*log(x)^2*log(3+
x)-15*x*log(x)^2+(-6*x^2-18*x)*exp(2)*log(x)+(-6*x^2-18*x)*exp(2)-6*x^3-18*x^2)/(x^4+3*x^3)/log(x)^2,x, algori
thm="maxima")

[Out]

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

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {15\,x\,{\ln \relax (x)}^2+{\mathrm {e}}^2\,\left (6\,x^2+18\,x\right )+18\,x^2+6\,x^3+{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (3\,x\,{\ln \relax (x)}^2-\ln \left (x+3\right )\,{\ln \relax (x)}^2\,\left (6\,x-{\mathrm {e}}^x\,\left (3\,x^2+9\,x\right )+18\right )\right )+{\mathrm {e}}^2\,\ln \relax (x)\,\left (6\,x^2+18\,x\right )-\ln \left (x+3\right )\,{\ln \relax (x)}^2\,\left (30\,x+90\right )}{{\ln \relax (x)}^2\,\left (x^4+3\,x^3\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(15*x*log(x)^2 + exp(2)*(18*x + 6*x^2) + 18*x^2 + 6*x^3 + exp(exp(x))*(3*x*log(x)^2 - log(x + 3)*log(x)^2
*(6*x - exp(x)*(9*x + 3*x^2) + 18)) + exp(2)*log(x)*(18*x + 6*x^2) - log(x + 3)*log(x)^2*(30*x + 90))/(log(x)^
2*(3*x^3 + x^4)),x)

[Out]

int(-(15*x*log(x)^2 + exp(2)*(18*x + 6*x^2) + 18*x^2 + 6*x^3 + exp(exp(x))*(3*x*log(x)^2 - log(x + 3)*log(x)^2
*(6*x - exp(x)*(9*x + 3*x^2) + 18)) + exp(2)*log(x)*(18*x + 6*x^2) - log(x + 3)*log(x)^2*(30*x + 90))/(log(x)^
2*(3*x^3 + x^4)), x)

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sympy [A]  time = 0.64, size = 37, normalized size = 1.12 \begin {gather*} \frac {6 x + 6 e^{2}}{x \log {\relax (x )}} - \frac {3 e^{e^{x}} \log {\left (x + 3 \right )}}{x^{2}} - \frac {15 \log {\left (x + 3 \right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-3*x**2-9*x)*exp(x)+18+6*x)*ln(x)**2*ln(3+x)-3*x*ln(x)**2)*exp(exp(x))+(30*x+90)*ln(x)**2*ln(3+x
)-15*x*ln(x)**2+(-6*x**2-18*x)*exp(2)*ln(x)+(-6*x**2-18*x)*exp(2)-6*x**3-18*x**2)/(x**4+3*x**3)/ln(x)**2,x)

[Out]

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

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