3.93.49 \(\int \frac {-54 x-108 x^2-60 x^3-21 x^4-3 x^5+e^3 (-3 x^3+x^4)+(3 x^3-x^4) \log (x)+(216 x+306 x^2+123 x^3+23 x^4+2 x^5+e^3 (-54 x-63 x^2-15 x^3-2 x^4)+(54 x+63 x^2+15 x^3+2 x^4) \log (x)) \log (4-e^3+x+\log (x))+(36 x-3 x^2-3 x^3+e^3 (-9 x+3 x^2)+(9 x-3 x^2) \log (x)) \log ^2(4-e^3+x+\log (x))+(12+e^3 (-3+x)-x-x^2+(3-x) \log (x)) \log ^3(4-e^3+x+\log (x))}{108 x^3+135 x^4+63 x^5+13 x^6+x^7+e^3 (-27 x^3-27 x^4-9 x^5-x^6)+(27 x^3+27 x^4+9 x^5+x^6) \log (x)+(324 x^2+405 x^3+189 x^4+39 x^5+3 x^6+e^3 (-81 x^2-81 x^3-27 x^4-3 x^5)+(81 x^2+81 x^3+27 x^4+3 x^5) \log (x)) \log (4-e^3+x+\log (x))+(324 x+405 x^2+189 x^3+39 x^4+3 x^5+e^3 (-81 x-81 x^2-27 x^3-3 x^4)+(81 x+81 x^2+27 x^3+3 x^4) \log (x)) \log ^2(4-e^3+x+\log (x))+(108+135 x+63 x^2+13 x^3+x^4+e^3 (-27-27 x-9 x^2-x^3)+(27+27 x+9 x^2+x^3) \log (x)) \log ^3(4-e^3+x+\log (x))} \, dx\)

Optimal. Leaf size=27 \[ \frac {x}{(3+x)^2}+\frac {x^2}{\left (x+\log \left (4-e^3+x+\log (x)\right )\right )^2} \]

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Rubi [F]  time = 5.50, 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 {-54 x-108 x^2-60 x^3-21 x^4-3 x^5+e^3 \left (-3 x^3+x^4\right )+\left (3 x^3-x^4\right ) \log (x)+\left (216 x+306 x^2+123 x^3+23 x^4+2 x^5+e^3 \left (-54 x-63 x^2-15 x^3-2 x^4\right )+\left (54 x+63 x^2+15 x^3+2 x^4\right ) \log (x)\right ) \log \left (4-e^3+x+\log (x)\right )+\left (36 x-3 x^2-3 x^3+e^3 \left (-9 x+3 x^2\right )+\left (9 x-3 x^2\right ) \log (x)\right ) \log ^2\left (4-e^3+x+\log (x)\right )+\left (12+e^3 (-3+x)-x-x^2+(3-x) \log (x)\right ) \log ^3\left (4-e^3+x+\log (x)\right )}{108 x^3+135 x^4+63 x^5+13 x^6+x^7+e^3 \left (-27 x^3-27 x^4-9 x^5-x^6\right )+\left (27 x^3+27 x^4+9 x^5+x^6\right ) \log (x)+\left (324 x^2+405 x^3+189 x^4+39 x^5+3 x^6+e^3 \left (-81 x^2-81 x^3-27 x^4-3 x^5\right )+\left (81 x^2+81 x^3+27 x^4+3 x^5\right ) \log (x)\right ) \log \left (4-e^3+x+\log (x)\right )+\left (324 x+405 x^2+189 x^3+39 x^4+3 x^5+e^3 \left (-81 x-81 x^2-27 x^3-3 x^4\right )+\left (81 x+81 x^2+27 x^3+3 x^4\right ) \log (x)\right ) \log ^2\left (4-e^3+x+\log (x)\right )+\left (108+135 x+63 x^2+13 x^3+x^4+e^3 \left (-27-27 x-9 x^2-x^3\right )+\left (27+27 x+9 x^2+x^3\right ) \log (x)\right ) \log ^3\left (4-e^3+x+\log (x)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-54*x - 108*x^2 - 60*x^3 - 21*x^4 - 3*x^5 + E^3*(-3*x^3 + x^4) + (3*x^3 - x^4)*Log[x] + (216*x + 306*x^2
+ 123*x^3 + 23*x^4 + 2*x^5 + E^3*(-54*x - 63*x^2 - 15*x^3 - 2*x^4) + (54*x + 63*x^2 + 15*x^3 + 2*x^4)*Log[x])*
Log[4 - E^3 + x + Log[x]] + (36*x - 3*x^2 - 3*x^3 + E^3*(-9*x + 3*x^2) + (9*x - 3*x^2)*Log[x])*Log[4 - E^3 + x
+ Log[x]]^2 + (12 + E^3*(-3 + x) - x - x^2 + (3 - x)*Log[x])*Log[4 - E^3 + x + Log[x]]^3)/(108*x^3 + 135*x^4
+ 63*x^5 + 13*x^6 + x^7 + E^3*(-27*x^3 - 27*x^4 - 9*x^5 - x^6) + (27*x^3 + 27*x^4 + 9*x^5 + x^6)*Log[x] + (324
*x^2 + 405*x^3 + 189*x^4 + 39*x^5 + 3*x^6 + E^3*(-81*x^2 - 81*x^3 - 27*x^4 - 3*x^5) + (81*x^2 + 81*x^3 + 27*x^
4 + 3*x^5)*Log[x])*Log[4 - E^3 + x + Log[x]] + (324*x + 405*x^2 + 189*x^3 + 39*x^4 + 3*x^5 + E^3*(-81*x - 81*x
^2 - 27*x^3 - 3*x^4) + (81*x + 81*x^2 + 27*x^3 + 3*x^4)*Log[x])*Log[4 - E^3 + x + Log[x]]^2 + (108 + 135*x + 6
3*x^2 + 13*x^3 + x^4 + E^3*(-27 - 27*x - 9*x^2 - x^3) + (27 + 27*x + 9*x^2 + x^3)*Log[x])*Log[4 - E^3 + x + Lo
g[x]]^3),x]

[Out]

x/(3 + x)^2 + 2*Defer[Int][x/((-4*(1 - E^3/4) - x - Log[x])*(x + Log[4 - E^3 + x + Log[x]])^3), x] + 2*Defer[I
nt][x^3/((-4*(1 - E^3/4) - x - Log[x])*(x + Log[4 - E^3 + x + Log[x]])^3), x] + 2*Defer[Int][(x^2*Log[x])/((-4
*(1 - E^3/4) - x - Log[x])*(x + Log[4 - E^3 + x + Log[x]])^3), x] - 2*(5 - E^3)*Defer[Int][x^2/((4*(1 - E^3/4)
+ x + Log[x])*(x + Log[4 - E^3 + x + Log[x]])^3), x] + 2*Defer[Int][x/(x + Log[4 - E^3 + x + Log[x]])^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-x \left (54+108 x+3 \left (20+e^3\right ) x^2-\left (-21+e^3\right ) x^3+3 x^4\right )-\left (-4+e^3-x\right ) x \left (54+63 x+15 x^2+2 x^3\right ) \log \left (4-e^3+x+\log (x)\right )-3 x \left (-12-e^3 (-3+x)+x+x^2\right ) \log ^2\left (4-e^3+x+\log (x)\right )+\left (12+e^3 (-3+x)-x-x^2\right ) \log ^3\left (4-e^3+x+\log (x)\right )+\log (x) \left (-\left ((-3+x) x^3\right )+x \left (54+63 x+15 x^2+2 x^3\right ) \log \left (4-e^3+x+\log (x)\right )-3 (-3+x) x \log ^2\left (4-e^3+x+\log (x)\right )-(-3+x) \log ^3\left (4-e^3+x+\log (x)\right )\right )}{(3+x)^3 \left (4 \left (1-\frac {e^3}{4}\right )+x+\log (x)\right ) \left (x+\log \left (4-e^3+x+\log (x)\right )\right )^3} \, dx\\ &=\int \left (\frac {3-x}{(3+x)^3}+\frac {2 x \left (-1-5 \left (1-\frac {e^3}{5}\right ) x-x^2-x \log (x)\right )}{\left (4 \left (1-\frac {e^3}{4}\right )+x+\log (x)\right ) \left (x+\log \left (4-e^3+x+\log (x)\right )\right )^3}+\frac {2 x}{\left (x+\log \left (4-e^3+x+\log (x)\right )\right )^2}\right ) \, dx\\ &=2 \int \frac {x \left (-1-5 \left (1-\frac {e^3}{5}\right ) x-x^2-x \log (x)\right )}{\left (4 \left (1-\frac {e^3}{4}\right )+x+\log (x)\right ) \left (x+\log \left (4-e^3+x+\log (x)\right )\right )^3} \, dx+2 \int \frac {x}{\left (x+\log \left (4-e^3+x+\log (x)\right )\right )^2} \, dx+\int \frac {3-x}{(3+x)^3} \, dx\\ &=\frac {x}{(3+x)^2}+2 \int \frac {x}{\left (x+\log \left (4-e^3+x+\log (x)\right )\right )^2} \, dx+2 \int \left (\frac {x}{\left (-4 \left (1-\frac {e^3}{4}\right )-x-\log (x)\right ) \left (x+\log \left (4-e^3+x+\log (x)\right )\right )^3}+\frac {x^3}{\left (-4 \left (1-\frac {e^3}{4}\right )-x-\log (x)\right ) \left (x+\log \left (4-e^3+x+\log (x)\right )\right )^3}+\frac {x^2 \log (x)}{\left (-4 \left (1-\frac {e^3}{4}\right )-x-\log (x)\right ) \left (x+\log \left (4-e^3+x+\log (x)\right )\right )^3}+\frac {\left (-5+e^3\right ) x^2}{\left (4 \left (1-\frac {e^3}{4}\right )+x+\log (x)\right ) \left (x+\log \left (4-e^3+x+\log (x)\right )\right )^3}\right ) \, dx\\ &=\frac {x}{(3+x)^2}+2 \int \frac {x}{\left (-4 \left (1-\frac {e^3}{4}\right )-x-\log (x)\right ) \left (x+\log \left (4-e^3+x+\log (x)\right )\right )^3} \, dx+2 \int \frac {x^3}{\left (-4 \left (1-\frac {e^3}{4}\right )-x-\log (x)\right ) \left (x+\log \left (4-e^3+x+\log (x)\right )\right )^3} \, dx+2 \int \frac {x^2 \log (x)}{\left (-4 \left (1-\frac {e^3}{4}\right )-x-\log (x)\right ) \left (x+\log \left (4-e^3+x+\log (x)\right )\right )^3} \, dx+2 \int \frac {x}{\left (x+\log \left (4-e^3+x+\log (x)\right )\right )^2} \, dx-\left (2 \left (5-e^3\right )\right ) \int \frac {x^2}{\left (4 \left (1-\frac {e^3}{4}\right )+x+\log (x)\right ) \left (x+\log \left (4-e^3+x+\log (x)\right )\right )^3} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.20, size = 25, normalized size = 0.93 \begin {gather*} x \left (\frac {1}{(3+x)^2}+\frac {x}{\left (x+\log \left (4-e^3+x+\log (x)\right )\right )^2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-54*x - 108*x^2 - 60*x^3 - 21*x^4 - 3*x^5 + E^3*(-3*x^3 + x^4) + (3*x^3 - x^4)*Log[x] + (216*x + 30
6*x^2 + 123*x^3 + 23*x^4 + 2*x^5 + E^3*(-54*x - 63*x^2 - 15*x^3 - 2*x^4) + (54*x + 63*x^2 + 15*x^3 + 2*x^4)*Lo
g[x])*Log[4 - E^3 + x + Log[x]] + (36*x - 3*x^2 - 3*x^3 + E^3*(-9*x + 3*x^2) + (9*x - 3*x^2)*Log[x])*Log[4 - E
^3 + x + Log[x]]^2 + (12 + E^3*(-3 + x) - x - x^2 + (3 - x)*Log[x])*Log[4 - E^3 + x + Log[x]]^3)/(108*x^3 + 13
5*x^4 + 63*x^5 + 13*x^6 + x^7 + E^3*(-27*x^3 - 27*x^4 - 9*x^5 - x^6) + (27*x^3 + 27*x^4 + 9*x^5 + x^6)*Log[x]
+ (324*x^2 + 405*x^3 + 189*x^4 + 39*x^5 + 3*x^6 + E^3*(-81*x^2 - 81*x^3 - 27*x^4 - 3*x^5) + (81*x^2 + 81*x^3 +
27*x^4 + 3*x^5)*Log[x])*Log[4 - E^3 + x + Log[x]] + (324*x + 405*x^2 + 189*x^3 + 39*x^4 + 3*x^5 + E^3*(-81*x
- 81*x^2 - 27*x^3 - 3*x^4) + (81*x + 81*x^2 + 27*x^3 + 3*x^4)*Log[x])*Log[4 - E^3 + x + Log[x]]^2 + (108 + 135
*x + 63*x^2 + 13*x^3 + x^4 + E^3*(-27 - 27*x - 9*x^2 - x^3) + (27 + 27*x + 9*x^2 + x^3)*Log[x])*Log[4 - E^3 +
x + Log[x]]^3),x]

[Out]

x*((3 + x)^(-2) + x/(x + Log[4 - E^3 + x + Log[x]])^2)

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fricas [B]  time = 0.52, size = 105, normalized size = 3.89 \begin {gather*} \frac {x^{4} + 7 \, x^{3} + 2 \, x^{2} \log \left (x - e^{3} + \log \relax (x) + 4\right ) + x \log \left (x - e^{3} + \log \relax (x) + 4\right )^{2} + 9 \, x^{2}}{x^{4} + 6 \, x^{3} + {\left (x^{2} + 6 \, x + 9\right )} \log \left (x - e^{3} + \log \relax (x) + 4\right )^{2} + 9 \, x^{2} + 2 \, {\left (x^{3} + 6 \, x^{2} + 9 \, x\right )} \log \left (x - e^{3} + \log \relax (x) + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3-x)*log(x)+exp(3)*(x-3)-x^2-x+12)*log(log(x)-exp(3)+4+x)^3+((-3*x^2+9*x)*log(x)+(3*x^2-9*x)*exp(
3)-3*x^3-3*x^2+36*x)*log(log(x)-exp(3)+4+x)^2+((2*x^4+15*x^3+63*x^2+54*x)*log(x)+(-2*x^4-15*x^3-63*x^2-54*x)*e
xp(3)+2*x^5+23*x^4+123*x^3+306*x^2+216*x)*log(log(x)-exp(3)+4+x)+(-x^4+3*x^3)*log(x)+(x^4-3*x^3)*exp(3)-3*x^5-
21*x^4-60*x^3-108*x^2-54*x)/(((x^3+9*x^2+27*x+27)*log(x)+(-x^3-9*x^2-27*x-27)*exp(3)+x^4+13*x^3+63*x^2+135*x+1
08)*log(log(x)-exp(3)+4+x)^3+((3*x^4+27*x^3+81*x^2+81*x)*log(x)+(-3*x^4-27*x^3-81*x^2-81*x)*exp(3)+3*x^5+39*x^
4+189*x^3+405*x^2+324*x)*log(log(x)-exp(3)+4+x)^2+((3*x^5+27*x^4+81*x^3+81*x^2)*log(x)+(-3*x^5-27*x^4-81*x^3-8
1*x^2)*exp(3)+3*x^6+39*x^5+189*x^4+405*x^3+324*x^2)*log(log(x)-exp(3)+4+x)+(x^6+9*x^5+27*x^4+27*x^3)*log(x)+(-
x^6-9*x^5-27*x^4-27*x^3)*exp(3)+x^7+13*x^6+63*x^5+135*x^4+108*x^3),x, algorithm="fricas")

[Out]

(x^4 + 7*x^3 + 2*x^2*log(x - e^3 + log(x) + 4) + x*log(x - e^3 + log(x) + 4)^2 + 9*x^2)/(x^4 + 6*x^3 + (x^2 +
6*x + 9)*log(x - e^3 + log(x) + 4)^2 + 9*x^2 + 2*(x^3 + 6*x^2 + 9*x)*log(x - e^3 + log(x) + 4))

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giac [B]  time = 3.20, size = 148, normalized size = 5.48 \begin {gather*} \frac {x^{4} + 7 \, x^{3} + 2 \, x^{2} \log \left (x - e^{3} + \log \relax (x) + 4\right ) + x \log \left (x - e^{3} + \log \relax (x) + 4\right )^{2} + 9 \, x^{2}}{x^{4} + 2 \, x^{3} \log \left (x - e^{3} + \log \relax (x) + 4\right ) + x^{2} \log \left (x - e^{3} + \log \relax (x) + 4\right )^{2} + 6 \, x^{3} + 12 \, x^{2} \log \left (x - e^{3} + \log \relax (x) + 4\right ) + 6 \, x \log \left (x - e^{3} + \log \relax (x) + 4\right )^{2} + 9 \, x^{2} + 18 \, x \log \left (x - e^{3} + \log \relax (x) + 4\right ) + 9 \, \log \left (x - e^{3} + \log \relax (x) + 4\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3-x)*log(x)+exp(3)*(x-3)-x^2-x+12)*log(log(x)-exp(3)+4+x)^3+((-3*x^2+9*x)*log(x)+(3*x^2-9*x)*exp(
3)-3*x^3-3*x^2+36*x)*log(log(x)-exp(3)+4+x)^2+((2*x^4+15*x^3+63*x^2+54*x)*log(x)+(-2*x^4-15*x^3-63*x^2-54*x)*e
xp(3)+2*x^5+23*x^4+123*x^3+306*x^2+216*x)*log(log(x)-exp(3)+4+x)+(-x^4+3*x^3)*log(x)+(x^4-3*x^3)*exp(3)-3*x^5-
21*x^4-60*x^3-108*x^2-54*x)/(((x^3+9*x^2+27*x+27)*log(x)+(-x^3-9*x^2-27*x-27)*exp(3)+x^4+13*x^3+63*x^2+135*x+1
08)*log(log(x)-exp(3)+4+x)^3+((3*x^4+27*x^3+81*x^2+81*x)*log(x)+(-3*x^4-27*x^3-81*x^2-81*x)*exp(3)+3*x^5+39*x^
4+189*x^3+405*x^2+324*x)*log(log(x)-exp(3)+4+x)^2+((3*x^5+27*x^4+81*x^3+81*x^2)*log(x)+(-3*x^5-27*x^4-81*x^3-8
1*x^2)*exp(3)+3*x^6+39*x^5+189*x^4+405*x^3+324*x^2)*log(log(x)-exp(3)+4+x)+(x^6+9*x^5+27*x^4+27*x^3)*log(x)+(-
x^6-9*x^5-27*x^4-27*x^3)*exp(3)+x^7+13*x^6+63*x^5+135*x^4+108*x^3),x, algorithm="giac")

[Out]

(x^4 + 7*x^3 + 2*x^2*log(x - e^3 + log(x) + 4) + x*log(x - e^3 + log(x) + 4)^2 + 9*x^2)/(x^4 + 2*x^3*log(x - e
^3 + log(x) + 4) + x^2*log(x - e^3 + log(x) + 4)^2 + 6*x^3 + 12*x^2*log(x - e^3 + log(x) + 4) + 6*x*log(x - e^
3 + log(x) + 4)^2 + 9*x^2 + 18*x*log(x - e^3 + log(x) + 4) + 9*log(x - e^3 + log(x) + 4)^2)

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maple [A]  time = 0.09, size = 32, normalized size = 1.19

method	result	size
risch	\(\frac {x}{x^{2}+6 x +9}+\frac {x^{2}}{\left (x +\ln \left (\ln \relax (x )-{\mathrm e}^{3}+4+x \right )\right )^{2}}\)	\(32\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((3-x)*ln(x)+exp(3)*(x-3)-x^2-x+12)*ln(ln(x)-exp(3)+4+x)^3+((-3*x^2+9*x)*ln(x)+(3*x^2-9*x)*exp(3)-3*x^3-3
*x^2+36*x)*ln(ln(x)-exp(3)+4+x)^2+((2*x^4+15*x^3+63*x^2+54*x)*ln(x)+(-2*x^4-15*x^3-63*x^2-54*x)*exp(3)+2*x^5+2
3*x^4+123*x^3+306*x^2+216*x)*ln(ln(x)-exp(3)+4+x)+(-x^4+3*x^3)*ln(x)+(x^4-3*x^3)*exp(3)-3*x^5-21*x^4-60*x^3-10
8*x^2-54*x)/(((x^3+9*x^2+27*x+27)*ln(x)+(-x^3-9*x^2-27*x-27)*exp(3)+x^4+13*x^3+63*x^2+135*x+108)*ln(ln(x)-exp(
3)+4+x)^3+((3*x^4+27*x^3+81*x^2+81*x)*ln(x)+(-3*x^4-27*x^3-81*x^2-81*x)*exp(3)+3*x^5+39*x^4+189*x^3+405*x^2+32
4*x)*ln(ln(x)-exp(3)+4+x)^2+((3*x^5+27*x^4+81*x^3+81*x^2)*ln(x)+(-3*x^5-27*x^4-81*x^3-81*x^2)*exp(3)+3*x^6+39*
x^5+189*x^4+405*x^3+324*x^2)*ln(ln(x)-exp(3)+4+x)+(x^6+9*x^5+27*x^4+27*x^3)*ln(x)+(-x^6-9*x^5-27*x^4-27*x^3)*e
xp(3)+x^7+13*x^6+63*x^5+135*x^4+108*x^3),x,method=_RETURNVERBOSE)

[Out]

x/(x^2+6*x+9)+x^2/(x+ln(ln(x)-exp(3)+4+x))^2

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maxima [B]  time = 0.57, size = 105, normalized size = 3.89 \begin {gather*} \frac {x^{4} + 7 \, x^{3} + 2 \, x^{2} \log \left (x - e^{3} + \log \relax (x) + 4\right ) + x \log \left (x - e^{3} + \log \relax (x) + 4\right )^{2} + 9 \, x^{2}}{x^{4} + 6 \, x^{3} + {\left (x^{2} + 6 \, x + 9\right )} \log \left (x - e^{3} + \log \relax (x) + 4\right )^{2} + 9 \, x^{2} + 2 \, {\left (x^{3} + 6 \, x^{2} + 9 \, x\right )} \log \left (x - e^{3} + \log \relax (x) + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3-x)*log(x)+exp(3)*(x-3)-x^2-x+12)*log(log(x)-exp(3)+4+x)^3+((-3*x^2+9*x)*log(x)+(3*x^2-9*x)*exp(
3)-3*x^3-3*x^2+36*x)*log(log(x)-exp(3)+4+x)^2+((2*x^4+15*x^3+63*x^2+54*x)*log(x)+(-2*x^4-15*x^3-63*x^2-54*x)*e
xp(3)+2*x^5+23*x^4+123*x^3+306*x^2+216*x)*log(log(x)-exp(3)+4+x)+(-x^4+3*x^3)*log(x)+(x^4-3*x^3)*exp(3)-3*x^5-
21*x^4-60*x^3-108*x^2-54*x)/(((x^3+9*x^2+27*x+27)*log(x)+(-x^3-9*x^2-27*x-27)*exp(3)+x^4+13*x^3+63*x^2+135*x+1
08)*log(log(x)-exp(3)+4+x)^3+((3*x^4+27*x^3+81*x^2+81*x)*log(x)+(-3*x^4-27*x^3-81*x^2-81*x)*exp(3)+3*x^5+39*x^
4+189*x^3+405*x^2+324*x)*log(log(x)-exp(3)+4+x)^2+((3*x^5+27*x^4+81*x^3+81*x^2)*log(x)+(-3*x^5-27*x^4-81*x^3-8
1*x^2)*exp(3)+3*x^6+39*x^5+189*x^4+405*x^3+324*x^2)*log(log(x)-exp(3)+4+x)+(x^6+9*x^5+27*x^4+27*x^3)*log(x)+(-
x^6-9*x^5-27*x^4-27*x^3)*exp(3)+x^7+13*x^6+63*x^5+135*x^4+108*x^3),x, algorithm="maxima")

[Out]

(x^4 + 7*x^3 + 2*x^2*log(x - e^3 + log(x) + 4) + x*log(x - e^3 + log(x) + 4)^2 + 9*x^2)/(x^4 + 6*x^3 + (x^2 +
6*x + 9)*log(x - e^3 + log(x) + 4)^2 + 9*x^2 + 2*(x^3 + 6*x^2 + 9*x)*log(x - e^3 + log(x) + 4))

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mupad [B]  time = 12.52, size = 1690, normalized size = 62.59 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(54*x - log(x)*(3*x^3 - x^4) + log(x - exp(3) + log(x) + 4)^3*(x + log(x)*(x - 3) - exp(3)*(x - 3) + x^2
- 12) - log(x - exp(3) + log(x) + 4)*(216*x + log(x)*(54*x + 63*x^2 + 15*x^3 + 2*x^4) - exp(3)*(54*x + 63*x^2
+ 15*x^3 + 2*x^4) + 306*x^2 + 123*x^3 + 23*x^4 + 2*x^5) + log(x - exp(3) + log(x) + 4)^2*(exp(3)*(9*x - 3*x^2)
- 36*x - log(x)*(9*x - 3*x^2) + 3*x^2 + 3*x^3) + exp(3)*(3*x^3 - x^4) + 108*x^2 + 60*x^3 + 21*x^4 + 3*x^5)/(l
og(x)*(27*x^3 + 27*x^4 + 9*x^5 + x^6) + log(x - exp(3) + log(x) + 4)*(log(x)*(81*x^2 + 81*x^3 + 27*x^4 + 3*x^5
) + 324*x^2 + 405*x^3 + 189*x^4 + 39*x^5 + 3*x^6 - exp(3)*(81*x^2 + 81*x^3 + 27*x^4 + 3*x^5)) + log(x - exp(3)
+ log(x) + 4)^2*(324*x + log(x)*(81*x + 81*x^2 + 27*x^3 + 3*x^4) - exp(3)*(81*x + 81*x^2 + 27*x^3 + 3*x^4) +
405*x^2 + 189*x^3 + 39*x^4 + 3*x^5) - exp(3)*(27*x^3 + 27*x^4 + 9*x^5 + x^6) + log(x - exp(3) + log(x) + 4)^3*
(135*x - exp(3)*(27*x + 9*x^2 + x^3 + 27) + log(x)*(27*x + 9*x^2 + x^3 + 27) + 63*x^2 + 13*x^3 + x^4 + 108) +
108*x^3 + 135*x^4 + 63*x^5 + 13*x^6 + x^7),x)

[Out]

((217*x + 30*exp(3) - 4*exp(6) - 94*x*exp(3) + 11*x*exp(6) - 225*x^2*exp(3) - 182*x^3*exp(3) - 20*x^4*exp(3) +
28*x^2*exp(6) + 14*x^5*exp(3) + 29*x^3*exp(6) + 4*x^6*exp(3) + 3*x^4*exp(6) - x^2*exp(9) - 2*x^3*exp(9) + 533
*x^2 + 411*x^3 + 40*x^4 - 66*x^5 - 25*x^6 - 2*x^7 - 51)/(6*(x + x^2 - 1)^3) + (log(x)*(94*x + 8*exp(3) - 22*x*
exp(3) - 56*x^2*exp(3) - 58*x^3*exp(3) - 6*x^4*exp(3) + 3*x^2*exp(6) + 6*x^3*exp(6) + 225*x^2 + 182*x^3 + 20*x
^4 - 14*x^5 - 4*x^6 - 30))/(6*(x + x^2 - 1)^3) + (log(x)^2*(11*x - 3*x^2*exp(3) - 6*x^3*exp(3) + 28*x^2 + 29*x
^3 + 3*x^4 - 4))/(6*(x + x^2 - 1)^3) + (x^2*log(x)^3*(2*x + 1))/(6*(x + x^2 - 1)^3))/(log(x)^2 + (5*x - x*exp(
3) + x^2 + 1)^2/x^2 + (2*log(x)*(5*x - x*exp(3) + x^2 + 1))/x) - (log(x)^3/(3*(x + x^2 - 1)) + (174*x - 38*exp
(3) + 4*exp(6) - 77*x*exp(3) + 13*x*exp(6) - x*exp(9) - 56*x^2*exp(3) - 30*x^3*exp(3) - 4*x^4*exp(3) + 6*x^2*e
xp(6) + 3*x^3*exp(6) + 151*x^2 + 83*x^3 + 18*x^4 + x^5 + 89)/(3*x*(x + x^2 - 1)) + (log(x)^2*(13*x - 3*x*exp(3
) + 6*x^2 + 3*x^3 + 4))/(3*x*(x + x^2 - 1)) + (log(x)*(77*x - 8*exp(3) - 26*x*exp(3) + 3*x*exp(6) - 12*x^2*exp
(3) - 6*x^3*exp(3) + 56*x^2 + 30*x^3 + 4*x^4 + 38))/(3*x*(x + x^2 - 1)))/(log(x)^3 + (5*x - x*exp(3) + x^2 + 1
)^3/x^3 + (3*log(x)^2*(5*x - x*exp(3) + x^2 + 1))/x + (3*log(x)*(5*x - x*exp(3) + x^2 + 1)^2)/x^2) - ((x*(188*
x + 8*exp(3) - 34*x*exp(3) - x*exp(6) - 500*x^2*exp(3) - 1221*x^3*exp(3) - 872*x^4*exp(3) + 57*x^2*exp(6) - 39
2*x^5*exp(3) + 173*x^3*exp(6) - 38*x^6*exp(3) + 115*x^4*exp(6) + 2*x^7*exp(3) - 2*x^2*exp(9) + 78*x^5*exp(6) -
7*x^3*exp(9) + 6*x^6*exp(6) - 4*x^4*exp(9) - 6*x^5*exp(9) + 1355*x^2 + 2714*x^3 + 1905*x^4 + 647*x^5 + 52*x^6
+ 13*x^7 + 12*x^8 + 2*x^9 - 30))/(6*(x + x^2 - 1)^5) + (x*log(x)*(34*x + 2*x*exp(3) - 114*x^2*exp(3) - 346*x^
3*exp(3) - 230*x^4*exp(3) + 6*x^2*exp(6) - 156*x^5*exp(3) + 21*x^3*exp(6) - 12*x^6*exp(3) + 12*x^4*exp(6) + 18
*x^5*exp(6) + 500*x^2 + 1221*x^3 + 872*x^4 + 392*x^5 + 38*x^6 - 2*x^7 - 8))/(6*(x + x^2 - 1)^5) + (x^3*log(x)^
3*(7*x + 4*x^2 + 6*x^3 + 2))/(6*(x + x^2 - 1)^5) + (x^2*log(x)^2*(57*x - 6*x*exp(3) - 21*x^2*exp(3) - 12*x^3*e
xp(3) - 18*x^4*exp(3) + 173*x^2 + 115*x^3 + 78*x^4 + 6*x^5 - 1))/(6*(x + x^2 - 1)^5))/(log(x) + (5*x - x*exp(3
) + x^2 + 1)/x) + ((x*(x + x^2))/(5*x - x*exp(3) + x*log(x) + x^2 + 1) - (x^2*log(x - exp(3) + log(x) + 4)*(x
- exp(3) + log(x) + 4))/(5*x - x*exp(3) + x*log(x) + x^2 + 1))/(log(x - exp(3) + log(x) + 4)^2 + 2*x*log(x - e
xp(3) + log(x) + 4) + x^2) + ((x*(x - exp(3) + log(x) + 4)*(x + x^3*log(x) - x^3*exp(3) + x^2 + 3*x^3))/(5*x -
x*exp(3) + x*log(x) + x^2 + 1)^3 - (x*log(x - exp(3) + log(x) + 4)*(x - exp(3) + log(x) + 4)*(9*x + 9*x^2*log
(x) + 2*x^3*log(x) - 2*x*exp(3) + x^2*log(x)^2 - 9*x^2*exp(3) - 2*x^3*exp(3) + x^2*exp(6) + 2*x*log(x) + 24*x^
2 + 10*x^3 + x^4 - 2*x^2*exp(3)*log(x)))/(5*x - x*exp(3) + x*log(x) + x^2 + 1)^3)/(x + log(x - exp(3) + log(x)
+ 4)) + (x^7*(40*exp(6) - 298*exp(3) + 511) - x^8*(27*exp(3) - 6*exp(6) + 4) - 240*x + x^3*(18*exp(6) - 336*e
xp(3) + 2043) + x^6*(85*exp(6) - 980*exp(3) + 2523) + x^5*(80*exp(6) - 1600*exp(3) + 5121) + x^4*(75*exp(6) -
1469*exp(3) + 5299) + x^9*(2*exp(3) + 33) + x^2*(36*exp(3) - 27) + 31*x^10 + 6*x^11 + 54)/(234*x - 96*x^2 - 69
0*x^3 + 420*x^4 + 1074*x^5 - 324*x^6 - 1014*x^7 - 180*x^8 + 390*x^9 + 264*x^10 + 66*x^11 + 6*x^12 - 54) - (log
(x)*(x^6*(2*exp(3) - 13/2) + x^3*((2*exp(3))/3 - 20/3) + x^5*((4*exp(3))/3 - 41/3) + x^4*((7*exp(3))/3 - 137/6
) + (2*x^2)/3 + x^7/3))/(5*x - 5*x^2 - 10*x^3 + 15*x^4 + 11*x^5 - 15*x^6 - 10*x^7 + 5*x^8 + 5*x^9 + x^10 - 1)
+ (log(x)^2*(x^3/3 + (7*x^4)/6 + (2*x^5)/3 + x^6))/(5*x - 5*x^2 - 10*x^3 + 15*x^4 + 11*x^5 - 15*x^6 - 10*x^7 +
5*x^8 + 5*x^9 + x^10 - 1)

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sympy [A]  time = 0.83, size = 44, normalized size = 1.63 \begin {gather*} \frac {x^{2}}{x^{2} + 2 x \log {\left (x + \log {\relax (x )} - e^{3} + 4 \right )} + \log {\left (x + \log {\relax (x )} - e^{3} + 4 \right )}^{2}} + \frac {x}{x^{2} + 6 x + 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3-x)*ln(x)+exp(3)*(x-3)-x**2-x+12)*ln(ln(x)-exp(3)+4+x)**3+((-3*x**2+9*x)*ln(x)+(3*x**2-9*x)*exp(
3)-3*x**3-3*x**2+36*x)*ln(ln(x)-exp(3)+4+x)**2+((2*x**4+15*x**3+63*x**2+54*x)*ln(x)+(-2*x**4-15*x**3-63*x**2-5
4*x)*exp(3)+2*x**5+23*x**4+123*x**3+306*x**2+216*x)*ln(ln(x)-exp(3)+4+x)+(-x**4+3*x**3)*ln(x)+(x**4-3*x**3)*ex
p(3)-3*x**5-21*x**4-60*x**3-108*x**2-54*x)/(((x**3+9*x**2+27*x+27)*ln(x)+(-x**3-9*x**2-27*x-27)*exp(3)+x**4+13
*x**3+63*x**2+135*x+108)*ln(ln(x)-exp(3)+4+x)**3+((3*x**4+27*x**3+81*x**2+81*x)*ln(x)+(-3*x**4-27*x**3-81*x**2
-81*x)*exp(3)+3*x**5+39*x**4+189*x**3+405*x**2+324*x)*ln(ln(x)-exp(3)+4+x)**2+((3*x**5+27*x**4+81*x**3+81*x**2
)*ln(x)+(-3*x**5-27*x**4-81*x**3-81*x**2)*exp(3)+3*x**6+39*x**5+189*x**4+405*x**3+324*x**2)*ln(ln(x)-exp(3)+4+
x)+(x**6+9*x**5+27*x**4+27*x**3)*ln(x)+(-x**6-9*x**5-27*x**4-27*x**3)*exp(3)+x**7+13*x**6+63*x**5+135*x**4+108
*x**3),x)

[Out]

x**2/(x**2 + 2*x*log(x + log(x) - exp(3) + 4) + log(x + log(x) - exp(3) + 4)**2) + x/(x**2 + 6*x + 9)

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