3.6.18 \(\int \frac {-495+2775 x-804 x^2-146 x^3+70 x^4-6 x^5+e (-125+825 x-465 x^2+91 x^3-6 x^4)+(-1485+522 x+45 x^2-33 x^3+3 x^4+e (-375+225 x-45 x^2+3 x^3)) \log (\frac {99-15 x-6 x^2+x^3+e (25-10 x+x^2)}{25-10 x+x^2})}{-495+174 x+15 x^2-11 x^3+x^4+e (-125+75 x-15 x^2+x^3)} \, dx\)

Optimal. Leaf size=29 \[ x \left (1+3 \left (-\frac {2}{x}-x+\log \left (4+e-\frac {1}{(5-x)^2}+x\right )\right )\right ) \]

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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[(-495 + 2775*x - 804*x^2 - 146*x^3 + 70*x^4 - 6*x^5 + E*(-125 + 825*x - 465*x^2 + 91*x^3 - 6*x^4) + (-1485
+ 522*x + 45*x^2 - 33*x^3 + 3*x^4 + E*(-375 + 225*x - 45*x^2 + 3*x^3))*Log[(99 - 15*x - 6*x^2 + x^3 + E*(25 -
10*x + x^2))/(25 - 10*x + x^2)])/(-495 + 174*x + 15*x^2 - 11*x^3 + x^4 + E*(-125 + 75*x - 15*x^2 + x^3)),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.11, size = 37, normalized size = 1.28 \begin {gather*} x-3 x^2+3 x \log \left (\frac {99+e (-5+x)^2-15 x-6 x^2+x^3}{(-5+x)^2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-495 + 2775*x - 804*x^2 - 146*x^3 + 70*x^4 - 6*x^5 + E*(-125 + 825*x - 465*x^2 + 91*x^3 - 6*x^4) +
(-1485 + 522*x + 45*x^2 - 33*x^3 + 3*x^4 + E*(-375 + 225*x - 45*x^2 + 3*x^3))*Log[(99 - 15*x - 6*x^2 + x^3 + E
*(25 - 10*x + x^2))/(25 - 10*x + x^2)])/(-495 + 174*x + 15*x^2 - 11*x^3 + x^4 + E*(-125 + 75*x - 15*x^2 + x^3)
),x]

[Out]

x - 3*x^2 + 3*x*Log[(99 + E*(-5 + x)^2 - 15*x - 6*x^2 + x^3)/(-5 + x)^2]

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fricas [A]  time = 0.88, size = 46, normalized size = 1.59 \begin {gather*} -3 \, x^{2} + 3 \, x \log \left (\frac {x^{3} - 6 \, x^{2} + {\left (x^{2} - 10 \, x + 25\right )} e - 15 \, x + 99}{x^{2} - 10 \, x + 25}\right ) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3*x^3-45*x^2+225*x-375)*exp(1)+3*x^4-33*x^3+45*x^2+522*x-1485)*log(((x^2-10*x+25)*exp(1)+x^3-6*x^
2-15*x+99)/(x^2-10*x+25))+(-6*x^4+91*x^3-465*x^2+825*x-125)*exp(1)-6*x^5+70*x^4-146*x^3-804*x^2+2775*x-495)/((
x^3-15*x^2+75*x-125)*exp(1)+x^4-11*x^3+15*x^2+174*x-495),x, algorithm="fricas")

[Out]

-3*x^2 + 3*x*log((x^3 - 6*x^2 + (x^2 - 10*x + 25)*e - 15*x + 99)/(x^2 - 10*x + 25)) + x

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giac [A]  time = 0.88, size = 50, normalized size = 1.72 \begin {gather*} -3 \, x^{2} + 3 \, x \log \left (\frac {x^{3} + x^{2} e - 6 \, x^{2} - 10 \, x e - 15 \, x + 25 \, e + 99}{x^{2} - 10 \, x + 25}\right ) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3*x^3-45*x^2+225*x-375)*exp(1)+3*x^4-33*x^3+45*x^2+522*x-1485)*log(((x^2-10*x+25)*exp(1)+x^3-6*x^
2-15*x+99)/(x^2-10*x+25))+(-6*x^4+91*x^3-465*x^2+825*x-125)*exp(1)-6*x^5+70*x^4-146*x^3-804*x^2+2775*x-495)/((
x^3-15*x^2+75*x-125)*exp(1)+x^4-11*x^3+15*x^2+174*x-495),x, algorithm="giac")

[Out]

-3*x^2 + 3*x*log((x^3 + x^2*e - 6*x^2 - 10*x*e - 15*x + 25*e + 99)/(x^2 - 10*x + 25)) + x

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maple [A]  time = 0.37, size = 47, normalized size = 1.62

method	result	size
norman	\(x -3 x^{2}+3 x \ln \left (\frac {\left (x^{2}-10 x +25\right ) {\mathrm e}+x^{3}-6 x^{2}-15 x +99}{x^{2}-10 x +25}\right )\)	\(47\)
risch	\(x -3 x^{2}+3 x \ln \left (\frac {\left (x^{2}-10 x +25\right ) {\mathrm e}+x^{3}-6 x^{2}-15 x +99}{x^{2}-10 x +25}\right )\)	\(47\)
default	\(-3 x^{2}+x -3 \left (\munderset {\textit {\_R} =\RootOf \left (\textit {\_Z}^{3}+\left ({\mathrm e}-6\right ) \textit {\_Z}^{2}+\left (-10 \,{\mathrm e}-15\right ) \textit {\_Z} +25 \,{\mathrm e}+99\right )}{\sum }\frac {\left (297+\textit {\_R}^{2} {\mathrm e}-20 \textit {\_R} \,{\mathrm e}-6 \textit {\_R}^{2}+75 \,{\mathrm e}-30 \textit {\_R} \right ) \ln \left (x -\textit {\_R} \right )}{2 \textit {\_R} \,{\mathrm e}+3 \textit {\_R}^{2}-10 \,{\mathrm e}-12 \textit {\_R} -15}\right )+3 \ln \left (\frac {x^{2} {\mathrm e}+x^{3}-10 x \,{\mathrm e}-6 x^{2}+25 \,{\mathrm e}-15 x +99}{x^{2}-10 x +25}\right ) x -3 \left (\munderset {\textit {\_R} =\RootOf \left (\textit {\_Z}^{3}+\left ({\mathrm e}-6\right ) \textit {\_Z}^{2}+\left (-10 \,{\mathrm e}-15\right ) \textit {\_Z} +25 \,{\mathrm e}+99\right )}{\sum }\frac {\left (-\textit {\_R}^{2} {\mathrm e}+20 \textit {\_R} \,{\mathrm e}+6 \textit {\_R}^{2}-75 \,{\mathrm e}+30 \textit {\_R} -297\right ) \ln \left (x -\textit {\_R} \right )}{2 \textit {\_R} \,{\mathrm e}+3 \textit {\_R}^{2}-10 \,{\mathrm e}-12 \textit {\_R} -15}\right )\)	\(220\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((3*x^3-45*x^2+225*x-375)*exp(1)+3*x^4-33*x^3+45*x^2+522*x-1485)*ln(((x^2-10*x+25)*exp(1)+x^3-6*x^2-15*x+
99)/(x^2-10*x+25))+(-6*x^4+91*x^3-465*x^2+825*x-125)*exp(1)-6*x^5+70*x^4-146*x^3-804*x^2+2775*x-495)/((x^3-15*
x^2+75*x-125)*exp(1)+x^4-11*x^3+15*x^2+174*x-495),x,method=_RETURNVERBOSE)

[Out]

x-3*x^2+3*x*ln(((x^2-10*x+25)*exp(1)+x^3-6*x^2-15*x+99)/(x^2-10*x+25))

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maxima [A]  time = 0.80, size = 44, normalized size = 1.52 \begin {gather*} -3 \, x^{2} + 3 \, x \log \left (x^{3} + x^{2} {\left (e - 6\right )} - 5 \, x {\left (2 \, e + 3\right )} + 25 \, e + 99\right ) - 6 \, x \log \left (x - 5\right ) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3*x^3-45*x^2+225*x-375)*exp(1)+3*x^4-33*x^3+45*x^2+522*x-1485)*log(((x^2-10*x+25)*exp(1)+x^3-6*x^
2-15*x+99)/(x^2-10*x+25))+(-6*x^4+91*x^3-465*x^2+825*x-125)*exp(1)-6*x^5+70*x^4-146*x^3-804*x^2+2775*x-495)/((
x^3-15*x^2+75*x-125)*exp(1)+x^4-11*x^3+15*x^2+174*x-495),x, algorithm="maxima")

[Out]

-3*x^2 + 3*x*log(x^3 + x^2*(e - 6) - 5*x*(2*e + 3) + 25*e + 99) - 6*x*log(x - 5) + x

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mupad [B]  time = 37.57, size = 46, normalized size = 1.59 \begin {gather*} x+3\,x\,\ln \left (\frac {\mathrm {e}\,\left (x^2-10\,x+25\right )-15\,x-6\,x^2+x^3+99}{x^2-10\,x+25}\right )-3\,x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(1)*(465*x^2 - 825*x - 91*x^3 + 6*x^4 + 125) - 2775*x + 804*x^2 + 146*x^3 - 70*x^4 + 6*x^5 - log((exp
(1)*(x^2 - 10*x + 25) - 15*x - 6*x^2 + x^3 + 99)/(x^2 - 10*x + 25))*(522*x + exp(1)*(225*x - 45*x^2 + 3*x^3 -
375) + 45*x^2 - 33*x^3 + 3*x^4 - 1485) + 495)/(174*x + exp(1)*(75*x - 15*x^2 + x^3 - 125) + 15*x^2 - 11*x^3 +
x^4 - 495),x)

[Out]

x + 3*x*log((exp(1)*(x^2 - 10*x + 25) - 15*x - 6*x^2 + x^3 + 99)/(x^2 - 10*x + 25)) - 3*x^2

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sympy [A]  time = 0.44, size = 44, normalized size = 1.52 \begin {gather*} - 3 x^{2} + 3 x \log {\left (\frac {x^{3} - 6 x^{2} - 15 x + e \left (x^{2} - 10 x + 25\right ) + 99}{x^{2} - 10 x + 25} \right )} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3*x**3-45*x**2+225*x-375)*exp(1)+3*x**4-33*x**3+45*x**2+522*x-1485)*ln(((x**2-10*x+25)*exp(1)+x**
3-6*x**2-15*x+99)/(x**2-10*x+25))+(-6*x**4+91*x**3-465*x**2+825*x-125)*exp(1)-6*x**5+70*x**4-146*x**3-804*x**2
+2775*x-495)/((x**3-15*x**2+75*x-125)*exp(1)+x**4-11*x**3+15*x**2+174*x-495),x)

[Out]

-3*x**2 + 3*x*log((x**3 - 6*x**2 - 15*x + E*(x**2 - 10*x + 25) + 99)/(x**2 - 10*x + 25)) + x

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