3.44.33 \(\int \frac {e^{3+e^5} (-20+12 x)+e^{3+e^5} (-20+24 x) \log (x)}{(25 x^2-30 x^3+9 x^4) \log ^2(x)} \, dx\)

Optimal. Leaf size=28 \[ \frac {e^{3+e^5}}{\left (-x+\frac {3}{4} (3-x) x\right ) \log (x)} \]

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Rubi [F]  time = 1.02, 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 {e^{3+e^5} (-20+12 x)+e^{3+e^5} (-20+24 x) \log (x)}{\left (25 x^2-30 x^3+9 x^4\right ) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(3 + E^5)*(-20 + 12*x) + E^(3 + E^5)*(-20 + 24*x)*Log[x])/((25*x^2 - 30*x^3 + 9*x^4)*Log[x]^2),x]

[Out]

4*E^(3 + E^5)*Defer[Int][1/(x^2*(-5 + 3*x)*Log[x]^2), x] + 4*E^(3 + E^5)*Defer[Int][(-5 + 6*x)/(x^2*(-5 + 3*x)
^2*Log[x]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{3+e^5} (-20+12 x)+e^{3+e^5} (-20+24 x) \log (x)}{x^2 \left (25-30 x+9 x^2\right ) \log ^2(x)} \, dx\\ &=\int \frac {e^{3+e^5} (-20+12 x)+e^{3+e^5} (-20+24 x) \log (x)}{x^2 (-5+3 x)^2 \log ^2(x)} \, dx\\ &=\int \frac {4 e^{3+e^5} (-5+3 x-5 \log (x)+6 x \log (x))}{(5-3 x)^2 x^2 \log ^2(x)} \, dx\\ &=\left (4 e^{3+e^5}\right ) \int \frac {-5+3 x-5 \log (x)+6 x \log (x)}{(5-3 x)^2 x^2 \log ^2(x)} \, dx\\ &=\left (4 e^{3+e^5}\right ) \int \left (\frac {1}{x^2 (-5+3 x) \log ^2(x)}+\frac {-5+6 x}{x^2 (-5+3 x)^2 \log (x)}\right ) \, dx\\ &=\left (4 e^{3+e^5}\right ) \int \frac {1}{x^2 (-5+3 x) \log ^2(x)} \, dx+\left (4 e^{3+e^5}\right ) \int \frac {-5+6 x}{x^2 (-5+3 x)^2 \log (x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.10, size = 23, normalized size = 0.82 \begin {gather*} -\frac {4 e^{3+e^5}}{x (-5+3 x) \log (x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(3 + E^5)*(-20 + 12*x) + E^(3 + E^5)*(-20 + 24*x)*Log[x])/((25*x^2 - 30*x^3 + 9*x^4)*Log[x]^2),x]

[Out]

(-4*E^(3 + E^5))/(x*(-5 + 3*x)*Log[x])

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fricas [A]  time = 0.66, size = 22, normalized size = 0.79 \begin {gather*} -\frac {4 \, e^{\left (e^{5} + 3\right )}}{{\left (3 \, x^{2} - 5 \, x\right )} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x-20)*exp(3)*exp(exp(5))*log(x)+(12*x-20)*exp(3)*exp(exp(5)))/(9*x^4-30*x^3+25*x^2)/log(x)^2,x,
algorithm="fricas")

[Out]

-4*e^(e^5 + 3)/((3*x^2 - 5*x)*log(x))

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giac [A]  time = 0.12, size = 22, normalized size = 0.79 \begin {gather*} -\frac {4 \, e^{\left (e^{5} + 3\right )}}{3 \, x^{2} \log \relax (x) - 5 \, x \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x-20)*exp(3)*exp(exp(5))*log(x)+(12*x-20)*exp(3)*exp(exp(5)))/(9*x^4-30*x^3+25*x^2)/log(x)^2,x,
algorithm="giac")

[Out]

-4*e^(e^5 + 3)/(3*x^2*log(x) - 5*x*log(x))

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maple [A]  time = 0.08, size = 22, normalized size = 0.79

method	result	size
norman	\(-\frac {4 \,{\mathrm e}^{3} {\mathrm e}^{{\mathrm e}^{5}}}{x \left (3 x -5\right ) \ln \relax (x )}\)	\(22\)
risch	\(-\frac {4 \,{\mathrm e}^{3+{\mathrm e}^{5}}}{\ln \relax (x ) \left (3 x -5\right ) x}\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((24*x-20)*exp(3)*exp(exp(5))*ln(x)+(12*x-20)*exp(3)*exp(exp(5)))/(9*x^4-30*x^3+25*x^2)/ln(x)^2,x,method=_
RETURNVERBOSE)

[Out]

-4*exp(3)*exp(exp(5))/x/(3*x-5)/ln(x)

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maxima [A]  time = 0.39, size = 22, normalized size = 0.79 \begin {gather*} -\frac {4 \, e^{\left (e^{5} + 3\right )}}{{\left (3 \, x^{2} - 5 \, x\right )} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x-20)*exp(3)*exp(exp(5))*log(x)+(12*x-20)*exp(3)*exp(exp(5)))/(9*x^4-30*x^3+25*x^2)/log(x)^2,x,
algorithm="maxima")

[Out]

-4*e^(e^5 + 3)/((3*x^2 - 5*x)*log(x))

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mupad [B]  time = 3.23, size = 33, normalized size = 1.18 \begin {gather*} \frac {4\,{\mathrm {e}}^{{\mathrm {e}}^5+3}}{5\,x\,\ln \relax (x)}-\frac {12\,{\mathrm {e}}^{{\mathrm {e}}^5+3}}{5\,\ln \relax (x)\,\left (3\,x-5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(3)*exp(exp(5))*(12*x - 20) + exp(3)*exp(exp(5))*log(x)*(24*x - 20))/(log(x)^2*(25*x^2 - 30*x^3 + 9*x^
4)),x)

[Out]

(4*exp(exp(5) + 3))/(5*x*log(x)) - (12*exp(exp(5) + 3))/(5*log(x)*(3*x - 5))

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sympy [A]  time = 0.13, size = 22, normalized size = 0.79 \begin {gather*} - \frac {4 e^{3} e^{e^{5}}}{\left (3 x^{2} - 5 x\right ) \log {\relax (x )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x-20)*exp(3)*exp(exp(5))*ln(x)+(12*x-20)*exp(3)*exp(exp(5)))/(9*x**4-30*x**3+25*x**2)/ln(x)**2,
x)

[Out]

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

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