∫ −3exx3+e2x(2x+x4)+(e2x(18−6x+36x3−12x4)+ex(−81x2+54x3−9x4)+(e2x(6−2x+12x3−4x4)+ex(−27x2+18x3−3x4)) log(3−x)) log(3+log(3−x))___________ −81x6+27x7+ex(108x4−36x5+54x7−18x8)+e2x(−36x2+12x3−36x5+12x6−9x8+3x9)+(−27x6+9x7+ex(36x4−12x5+18x7−6x8)+e2x(−12x2+4x3−12x5+4x6−3x8+x9)) log(3−x) dx

3.79.32 $\int \frac {-3 e^x x^3+e^{2 x} (2 x+x^4)+(e^{2 x} (18-6 x+36 x^3-12 x^4)+e^x (-81 x^2+54 x^3-9 x^4)+(e^{2 x} (6-2 x+12 x^3-4 x^4)+e^x (-27 x^2+18 x^3-3 x^4)) \log (3-x)) \log (3+\log (3-x))}{-81 x^6+27 x^7+e^x (108 x^4-36 x^5+54 x^7-18 x^8)+e^{2 x} (-36 x^2+12 x^3-36 x^5+12 x^6-9 x^8+3 x^9)+(-27 x^6+9 x^7+e^x (36 x^4-12 x^5+18 x^7-6 x^8)+e^{2 x} (-12 x^2+4 x^3-12 x^5+4 x^6-3 x^8+x^9)) \log (3-x)} \, dx$

Optimal. Leaf size=30 \[ \frac {\log (3+\log (3-x))}{x \left (2+x^2 \left (-3 e^{-x}+x\right )\right )} \]

________________________________________________________________________________________

Rubi [F] time = 180.00, 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[(-3*E^x*x^3 + E^(2*x)*(2*x + x^4) + (E^(2*x)*(18 - 6*x + 36*x^3 - 12*x^4) + E^x*(-81*x^2 + 54*x^3 - 9*x^4)

+ (E^(2*x)*(6 - 2*x + 12*x^3 - 4*x^4) + E^x*(-27*x^2 + 18*x^3 - 3*x^4))*Log[3 - x])*Log[3 + Log[3 - x]])/(-81

*x^6 + 27*x^7 + E^x*(108*x^4 - 36*x^5 + 54*x^7 - 18*x^8) + E^(2*x)*(-36*x^2 + 12*x^3 - 36*x^5 + 12*x^6 - 9*x^8

+ 3*x^9) + (-27*x^6 + 9*x^7 + E^x*(36*x^4 - 12*x^5 + 18*x^7 - 6*x^8) + E^(2*x)*(-12*x^2 + 4*x^3 - 12*x^5 + 4*

x^6 - 3*x^8 + x^9))*Log[3 - x]),x]

[Out]

$Aborted

Rubi steps

Aborted

________________________________________________________________________________________

Mathematica [A] time = 0.23, size = 31, normalized size = 1.03 \begin {gather*} \frac {e^x \log (3+\log (3-x))}{-3 x^3+e^x x \left (2+x^3\right )} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(-3*E^x*x^3 + E^(2*x)*(2*x + x^4) + (E^(2*x)*(18 - 6*x + 36*x^3 - 12*x^4) + E^x*(-81*x^2 + 54*x^3 -

9*x^4) + (E^(2*x)*(6 - 2*x + 12*x^3 - 4*x^4) + E^x*(-27*x^2 + 18*x^3 - 3*x^4))*Log[3 - x])*Log[3 + Log[3 - x]]

)/(-81*x^6 + 27*x^7 + E^x*(108*x^4 - 36*x^5 + 54*x^7 - 18*x^8) + E^(2*x)*(-36*x^2 + 12*x^3 - 36*x^5 + 12*x^6 -

9*x^8 + 3*x^9) + (-27*x^6 + 9*x^7 + E^x*(36*x^4 - 12*x^5 + 18*x^7 - 6*x^8) + E^(2*x)*(-12*x^2 + 4*x^3 - 12*x^

5 + 4*x^6 - 3*x^8 + x^9))*Log[3 - x]),x]

[Out]

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

________________________________________________________________________________________

fricas [A] time = 1.02, size = 32, normalized size = 1.07 \begin {gather*} -\frac {e^{x} \log \left (\log \left (-x + 3\right ) + 3\right )}{3 \, x^{3} - {\left (x^{4} + 2 \, x\right )} e^{x}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-4*x^4+12*x^3-2*x+6)*exp(x)^2+(-3*x^4+18*x^3-27*x^2)*exp(x))*log(3-x)+(-12*x^4+36*x^3-6*x+18)*ex

p(x)^2+(-9*x^4+54*x^3-81*x^2)*exp(x))*log(log(3-x)+3)+(x^4+2*x)*exp(x)^2-3*exp(x)*x^3)/(((x^9-3*x^8+4*x^6-12*x

^5+4*x^3-12*x^2)*exp(x)^2+(-6*x^8+18*x^7-12*x^5+36*x^4)*exp(x)+9*x^7-27*x^6)*log(3-x)+(3*x^9-9*x^8+12*x^6-36*x

^5+12*x^3-36*x^2)*exp(x)^2+(-18*x^8+54*x^7-36*x^5+108*x^4)*exp(x)+27*x^7-81*x^6),x, algorithm="fricas")

[Out]

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

________________________________________________________________________________________

giac [A] time = 0.29, size = 31, normalized size = 1.03 \begin {gather*} \frac {e^{x} \log \left (\log \left (-x + 3\right ) + 3\right )}{x^{4} e^{x} - 3 \, x^{3} + 2 \, x e^{x}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-4*x^4+12*x^3-2*x+6)*exp(x)^2+(-3*x^4+18*x^3-27*x^2)*exp(x))*log(3-x)+(-12*x^4+36*x^3-6*x+18)*ex

p(x)^2+(-9*x^4+54*x^3-81*x^2)*exp(x))*log(log(3-x)+3)+(x^4+2*x)*exp(x)^2-3*exp(x)*x^3)/(((x^9-3*x^8+4*x^6-12*x

^5+4*x^3-12*x^2)*exp(x)^2+(-6*x^8+18*x^7-12*x^5+36*x^4)*exp(x)+9*x^7-27*x^6)*log(3-x)+(3*x^9-9*x^8+12*x^6-36*x

^5+12*x^3-36*x^2)*exp(x)^2+(-18*x^8+54*x^7-36*x^5+108*x^4)*exp(x)+27*x^7-81*x^6),x, algorithm="giac")

[Out]

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

________________________________________________________________________________________

maple [A] time = 0.06, size = 34, normalized size = 1.13


method	result	size

risch	$\frac {{\mathrm e}^{x} \ln \left (\ln \left (3-x \right )+3\right )}{x \left ({\mathrm e}^{x} x^{3}-3 x^{2}+2 \,{\mathrm e}^{x}\right )}$	$34$

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((((-4*x^4+12*x^3-2*x+6)*exp(x)^2+(-3*x^4+18*x^3-27*x^2)*exp(x))*ln(3-x)+(-12*x^4+36*x^3-6*x+18)*exp(x)^2+

(-9*x^4+54*x^3-81*x^2)*exp(x))*ln(ln(3-x)+3)+(x^4+2*x)*exp(x)^2-3*exp(x)*x^3)/(((x^9-3*x^8+4*x^6-12*x^5+4*x^3-

12*x^2)*exp(x)^2+(-6*x^8+18*x^7-12*x^5+36*x^4)*exp(x)+9*x^7-27*x^6)*ln(3-x)+(3*x^9-9*x^8+12*x^6-36*x^5+12*x^3-

36*x^2)*exp(x)^2+(-18*x^8+54*x^7-36*x^5+108*x^4)*exp(x)+27*x^7-81*x^6),x,method=_RETURNVERBOSE)

[Out]

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

________________________________________________________________________________________

maxima [A] time = 0.49, size = 32, normalized size = 1.07 \begin {gather*} -\frac {e^{x} \log \left (\log \left (-x + 3\right ) + 3\right )}{3 \, x^{3} - {\left (x^{4} + 2 \, x\right )} e^{x}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-4*x^4+12*x^3-2*x+6)*exp(x)^2+(-3*x^4+18*x^3-27*x^2)*exp(x))*log(3-x)+(-12*x^4+36*x^3-6*x+18)*ex

p(x)^2+(-9*x^4+54*x^3-81*x^2)*exp(x))*log(log(3-x)+3)+(x^4+2*x)*exp(x)^2-3*exp(x)*x^3)/(((x^9-3*x^8+4*x^6-12*x

^5+4*x^3-12*x^2)*exp(x)^2+(-6*x^8+18*x^7-12*x^5+36*x^4)*exp(x)+9*x^7-27*x^6)*log(3-x)+(3*x^9-9*x^8+12*x^6-36*x

^5+12*x^3-36*x^2)*exp(x)^2+(-18*x^8+54*x^7-36*x^5+108*x^4)*exp(x)+27*x^7-81*x^6),x, algorithm="maxima")

[Out]

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

________________________________________________________________________________________

mupad [B] time = 5.93, size = 171, normalized size = 5.70 \begin {gather*} \frac {3\,\ln \left (\ln \left (3-x\right )+3\right )\,\left (3\,x^3-x^4\right )}{\left (x^3+2\right )\,\left ({\mathrm {e}}^x\,\left (-x^6+3\,x^5-2\,x^3+6\,x^2\right )-9\,x^4+3\,x^5\right )}-\frac {\ln \left (\ln \left (3-x\right )+3\right )\,\left (\frac {9\,x^4-3\,x^5}{x^4+2\,x}-\frac {{\mathrm {e}}^x\,\left (-x^6+3\,x^5-2\,x^3+6\,x^2\right )}{x^4+2\,x}\right )}{{\mathrm {e}}^x\,\left (-x^6+3\,x^5-2\,x^3+6\,x^2\right )-9\,x^4+3\,x^5} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((3*x^3*exp(x) + log(log(3 - x) + 3)*(exp(2*x)*(6*x - 36*x^3 + 12*x^4 - 18) + exp(x)*(81*x^2 - 54*x^3 + 9*x

^4) + log(3 - x)*(exp(2*x)*(2*x - 12*x^3 + 4*x^4 - 6) + exp(x)*(27*x^2 - 18*x^3 + 3*x^4))) - exp(2*x)*(2*x + x

^4))/(exp(2*x)*(36*x^2 - 12*x^3 + 36*x^5 - 12*x^6 + 9*x^8 - 3*x^9) - exp(x)*(108*x^4 - 36*x^5 + 54*x^7 - 18*x^

8) + log(3 - x)*(exp(2*x)*(12*x^2 - 4*x^3 + 12*x^5 - 4*x^6 + 3*x^8 - x^9) - exp(x)*(36*x^4 - 12*x^5 + 18*x^7 -

6*x^8) + 27*x^6 - 9*x^7) + 81*x^6 - 27*x^7),x)

[Out]

(3*log(log(3 - x) + 3)*(3*x^3 - x^4))/((x^3 + 2)*(exp(x)*(6*x^2 - 2*x^3 + 3*x^5 - x^6) - 9*x^4 + 3*x^5)) - (lo

g(log(3 - x) + 3)*((9*x^4 - 3*x^5)/(2*x + x^4) - (exp(x)*(6*x^2 - 2*x^3 + 3*x^5 - x^6))/(2*x + x^4)))/(exp(x)*

(6*x^2 - 2*x^3 + 3*x^5 - x^6) - 9*x^4 + 3*x^5)

________________________________________________________________________________________

sympy [B] time = 0.81, size = 49, normalized size = 1.63 \begin {gather*} \frac {3 x \log {\left (\log {\left (3 - x \right )} + 3 \right )}}{- 3 x^{5} - 6 x^{2} + \left (x^{6} + 4 x^{3} + 4\right ) e^{x}} + \frac {\log {\left (\log {\left (3 - x \right )} + 3 \right )}}{x^{4} + 2 x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-4*x**4+12*x**3-2*x+6)*exp(x)**2+(-3*x**4+18*x**3-27*x**2)*exp(x))*ln(3-x)+(-12*x**4+36*x**3-6*x

+18)*exp(x)**2+(-9*x**4+54*x**3-81*x**2)*exp(x))*ln(ln(3-x)+3)+(x**4+2*x)*exp(x)**2-3*exp(x)*x**3)/(((x**9-3*x

**8+4*x**6-12*x**5+4*x**3-12*x**2)*exp(x)**2+(-6*x**8+18*x**7-12*x**5+36*x**4)*exp(x)+9*x**7-27*x**6)*ln(3-x)+

(3*x**9-9*x**8+12*x**6-36*x**5+12*x**3-36*x**2)*exp(x)**2+(-18*x**8+54*x**7-36*x**5+108*x**4)*exp(x)+27*x**7-8

1*x**6),x)

[Out]

3*x*log(log(3 - x) + 3)/(-3*x**5 - 6*x**2 + (x**6 + 4*x**3 + 4)*exp(x)) + log(log(3 - x) + 3)/(x**4 + 2*x)

________________________________________________________________________________________

[next] [prev] [prev-tail] [front] [up]