3.77.28 \(\int \frac {(216+324 x+72 x^2-80 x^3-32 x^4) \log ^3(\frac {-24-25 x-6 x^2}{4+4 x+x^2})+(3456+9936 x+11304 x^2+6352 x^3+1760 x^4+192 x^5) \log ^4(\frac {-24-25 x-6 x^2}{4+4 x+x^2})}{16+14 x+3 x^2} \, dx\)

Optimal. Leaf size=21 \[ (3+2 x)^4 \log ^4\left (-6-\frac {x}{(2+x)^2}\right ) \]

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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[((216 + 324*x + 72*x^2 - 80*x^3 - 32*x^4)*Log[(-24 - 25*x - 6*x^2)/(4 + 4*x + x^2)]^3 + (3456 + 9936*x + 1
1304*x^2 + 6352*x^3 + 1760*x^4 + 192*x^5)*Log[(-24 - 25*x - 6*x^2)/(4 + 4*x + x^2)]^4)/(16 + 14*x + 3*x^2),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.07, size = 28, normalized size = 1.33 \begin {gather*} (3+2 x)^4 \log ^4\left (-\frac {24+25 x+6 x^2}{(2+x)^2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((216 + 324*x + 72*x^2 - 80*x^3 - 32*x^4)*Log[(-24 - 25*x - 6*x^2)/(4 + 4*x + x^2)]^3 + (3456 + 9936
*x + 11304*x^2 + 6352*x^3 + 1760*x^4 + 192*x^5)*Log[(-24 - 25*x - 6*x^2)/(4 + 4*x + x^2)]^4)/(16 + 14*x + 3*x^
2),x]

[Out]

(3 + 2*x)^4*Log[-((24 + 25*x + 6*x^2)/(2 + x)^2)]^4

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fricas [B]  time = 0.75, size = 46, normalized size = 2.19 \begin {gather*} {\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )} \log \left (-\frac {6 \, x^{2} + 25 \, x + 24}{x^{2} + 4 \, x + 4}\right )^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((192*x^5+1760*x^4+6352*x^3+11304*x^2+9936*x+3456)*log((-6*x^2-25*x-24)/(x^2+4*x+4))^4+(-32*x^4-80*x
^3+72*x^2+324*x+216)*log((-6*x^2-25*x-24)/(x^2+4*x+4))^3)/(3*x^2+14*x+16),x, algorithm="fricas")

[Out]

(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(-(6*x^2 + 25*x + 24)/(x^2 + 4*x + 4))^4

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giac [B]  time = 6.92, size = 46, normalized size = 2.19 \begin {gather*} {\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )} \log \left (-\frac {6 \, x^{2} + 25 \, x + 24}{x^{2} + 4 \, x + 4}\right )^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((192*x^5+1760*x^4+6352*x^3+11304*x^2+9936*x+3456)*log((-6*x^2-25*x-24)/(x^2+4*x+4))^4+(-32*x^4-80*x
^3+72*x^2+324*x+216)*log((-6*x^2-25*x-24)/(x^2+4*x+4))^3)/(3*x^2+14*x+16),x, algorithm="giac")

[Out]

(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(-(6*x^2 + 25*x + 24)/(x^2 + 4*x + 4))^4

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maple [F]  time = 0.08, size = 0, normalized size = 0.00 \[\int \frac {\left (192 x^{5}+1760 x^{4}+6352 x^{3}+11304 x^{2}+9936 x +3456\right ) \ln \left (\frac {-6 x^{2}-25 x -24}{x^{2}+4 x +4}\right )^{4}+\left (-32 x^{4}-80 x^{3}+72 x^{2}+324 x +216\right ) \ln \left (\frac {-6 x^{2}-25 x -24}{x^{2}+4 x +4}\right )^{3}}{3 x^{2}+14 x +16}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((192*x^5+1760*x^4+6352*x^3+11304*x^2+9936*x+3456)*ln((-6*x^2-25*x-24)/(x^2+4*x+4))^4+(-32*x^4-80*x^3+72*x
^2+324*x+216)*ln((-6*x^2-25*x-24)/(x^2+4*x+4))^3)/(3*x^2+14*x+16),x)

[Out]

int(((192*x^5+1760*x^4+6352*x^3+11304*x^2+9936*x+3456)*ln((-6*x^2-25*x-24)/(x^2+4*x+4))^4+(-32*x^4-80*x^3+72*x
^2+324*x+216)*ln((-6*x^2-25*x-24)/(x^2+4*x+4))^3)/(3*x^2+14*x+16),x)

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maxima [B]  time = 0.45, size = 491, normalized size = 23.38 \begin {gather*} {\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )} \log \left (2 \, x + 3\right )^{4} + 16 \, {\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )} \log \left (x + 2\right )^{4} - 32 \, {\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )} \log \left (x + 2\right )^{3} \log \left (-3 \, x - 8\right ) + 24 \, {\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )} \log \left (x + 2\right )^{2} \log \left (-3 \, x - 8\right )^{2} - 8 \, {\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )} \log \left (x + 2\right ) \log \left (-3 \, x - 8\right )^{3} + {\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )} \log \left (-3 \, x - 8\right )^{4} - 4 \, {\left (2 \, {\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )} \log \left (x + 2\right ) - {\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )} \log \left (-3 \, x - 8\right )\right )} \log \left (2 \, x + 3\right )^{3} + 6 \, {\left (4 \, {\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )} \log \left (x + 2\right )^{2} - 4 \, {\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )} \log \left (x + 2\right ) \log \left (-3 \, x - 8\right ) + {\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )} \log \left (-3 \, x - 8\right )^{2}\right )} \log \left (2 \, x + 3\right )^{2} - 4 \, {\left (8 \, {\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )} \log \left (x + 2\right )^{3} - 12 \, {\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )} \log \left (x + 2\right )^{2} \log \left (-3 \, x - 8\right ) + 6 \, {\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )} \log \left (x + 2\right ) \log \left (-3 \, x - 8\right )^{2} - {\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )} \log \left (-3 \, x - 8\right )^{3}\right )} \log \left (2 \, x + 3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((192*x^5+1760*x^4+6352*x^3+11304*x^2+9936*x+3456)*log((-6*x^2-25*x-24)/(x^2+4*x+4))^4+(-32*x^4-80*x
^3+72*x^2+324*x+216)*log((-6*x^2-25*x-24)/(x^2+4*x+4))^3)/(3*x^2+14*x+16),x, algorithm="maxima")

[Out]

(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(2*x + 3)^4 + 16*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(x +
2)^4 - 32*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(x + 2)^3*log(-3*x - 8) + 24*(16*x^4 + 96*x^3 + 216*x^2
+ 216*x + 81)*log(x + 2)^2*log(-3*x - 8)^2 - 8*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(x + 2)*log(-3*x -
8)^3 + (16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(-3*x - 8)^4 - 4*(2*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81
)*log(x + 2) - (16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(-3*x - 8))*log(2*x + 3)^3 + 6*(4*(16*x^4 + 96*x^3
+ 216*x^2 + 216*x + 81)*log(x + 2)^2 - 4*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(x + 2)*log(-3*x - 8) + (
16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(-3*x - 8)^2)*log(2*x + 3)^2 - 4*(8*(16*x^4 + 96*x^3 + 216*x^2 + 21
6*x + 81)*log(x + 2)^3 - 12*(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(x + 2)^2*log(-3*x - 8) + 6*(16*x^4 +
96*x^3 + 216*x^2 + 216*x + 81)*log(x + 2)*log(-3*x - 8)^2 - (16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)*log(-3*x
- 8)^3)*log(2*x + 3)

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mupad [B]  time = 6.12, size = 33, normalized size = 1.57 \begin {gather*} {\ln \left (-\frac {6\,x^2+25\,x+24}{x^2+4\,x+4}\right )}^4\,{\left (2\,x+3\right )}^4 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(-(25*x + 6*x^2 + 24)/(4*x + x^2 + 4))^3*(324*x + 72*x^2 - 80*x^3 - 32*x^4 + 216) + log(-(25*x + 6*x^2
+ 24)/(4*x + x^2 + 4))^4*(9936*x + 11304*x^2 + 6352*x^3 + 1760*x^4 + 192*x^5 + 3456))/(14*x + 3*x^2 + 16),x)

[Out]

log(-(25*x + 6*x^2 + 24)/(4*x + x^2 + 4))^4*(2*x + 3)^4

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sympy [B]  time = 0.28, size = 42, normalized size = 2.00 \begin {gather*} \left (16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81\right ) \log {\left (\frac {- 6 x^{2} - 25 x - 24}{x^{2} + 4 x + 4} \right )}^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((192*x**5+1760*x**4+6352*x**3+11304*x**2+9936*x+3456)*ln((-6*x**2-25*x-24)/(x**2+4*x+4))**4+(-32*x*
*4-80*x**3+72*x**2+324*x+216)*ln((-6*x**2-25*x-24)/(x**2+4*x+4))**3)/(3*x**2+14*x+16),x)

[Out]

(16*x**4 + 96*x**3 + 216*x**2 + 216*x + 81)*log((-6*x**2 - 25*x - 24)/(x**2 + 4*x + 4))**4

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