3.55.97 \(\int \frac {-7680-65280 x+3840 x \log (4 x)}{-6859 x+13718 x^2-6859 x^3+(1083 x-2166 x^2+1083 x^3) \log (4 x)+(-57 x+114 x^2-57 x^3) \log ^2(4 x)+(x-2 x^2+x^3) \log ^3(4 x)} \, dx\)

Optimal. Leaf size=17 \[ \frac {3840}{(1-x) (-19+\log (4 x))^2} \]

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Rubi [F]  time = 0.48, 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 {-7680-65280 x+3840 x \log (4 x)}{-6859 x+13718 x^2-6859 x^3+\left (1083 x-2166 x^2+1083 x^3\right ) \log (4 x)+\left (-57 x+114 x^2-57 x^3\right ) \log ^2(4 x)+\left (x-2 x^2+x^3\right ) \log ^3(4 x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-7680 - 65280*x + 3840*x*Log[4*x])/(-6859*x + 13718*x^2 - 6859*x^3 + (1083*x - 2166*x^2 + 1083*x^3)*Log[4
*x] + (-57*x + 114*x^2 - 57*x^3)*Log[4*x]^2 + (x - 2*x^2 + x^3)*Log[4*x]^3),x]

[Out]

7680*Defer[Int][1/((-1 + x)*x*(-19 + Log[4*x])^3), x] + 3840*Defer[Int][1/((-1 + x)^2*(-19 + Log[4*x])^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3840 (2+17 x-x \log (4 x))}{(1-x)^2 x (19-\log (4 x))^3} \, dx\\ &=3840 \int \frac {2+17 x-x \log (4 x)}{(1-x)^2 x (19-\log (4 x))^3} \, dx\\ &=3840 \int \left (\frac {2}{(-1+x) x (-19+\log (4 x))^3}+\frac {1}{(-1+x)^2 (-19+\log (4 x))^2}\right ) \, dx\\ &=3840 \int \frac {1}{(-1+x)^2 (-19+\log (4 x))^2} \, dx+7680 \int \frac {1}{(-1+x) x (-19+\log (4 x))^3} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.08, size = 17, normalized size = 1.00 \begin {gather*} \frac {3840}{(1-x) (-19+\log (4 x))^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-7680 - 65280*x + 3840*x*Log[4*x])/(-6859*x + 13718*x^2 - 6859*x^3 + (1083*x - 2166*x^2 + 1083*x^3)
*Log[4*x] + (-57*x + 114*x^2 - 57*x^3)*Log[4*x]^2 + (x - 2*x^2 + x^3)*Log[4*x]^3),x]

[Out]

3840/((1 - x)*(-19 + Log[4*x])^2)

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fricas [A]  time = 1.94, size = 28, normalized size = 1.65 \begin {gather*} -\frac {3840}{{\left (x - 1\right )} \log \left (4 \, x\right )^{2} - 38 \, {\left (x - 1\right )} \log \left (4 \, x\right ) + 361 \, x - 361} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3840*x*log(4*x)-65280*x-7680)/((x^3-2*x^2+x)*log(4*x)^3+(-57*x^3+114*x^2-57*x)*log(4*x)^2+(1083*x^3
-2166*x^2+1083*x)*log(4*x)-6859*x^3+13718*x^2-6859*x),x, algorithm="fricas")

[Out]

-3840/((x - 1)*log(4*x)^2 - 38*(x - 1)*log(4*x) + 361*x - 361)

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giac [B]  time = 0.26, size = 38, normalized size = 2.24 \begin {gather*} -\frac {3840}{x \log \left (4 \, x\right )^{2} - 38 \, x \log \left (4 \, x\right ) - \log \left (4 \, x\right )^{2} + 361 \, x + 38 \, \log \left (4 \, x\right ) - 361} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3840*x*log(4*x)-65280*x-7680)/((x^3-2*x^2+x)*log(4*x)^3+(-57*x^3+114*x^2-57*x)*log(4*x)^2+(1083*x^3
-2166*x^2+1083*x)*log(4*x)-6859*x^3+13718*x^2-6859*x),x, algorithm="giac")

[Out]

-3840/(x*log(4*x)^2 - 38*x*log(4*x) - log(4*x)^2 + 361*x + 38*log(4*x) - 361)

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maple [A]  time = 0.07, size = 16, normalized size = 0.94

method	result	size
norman	\(-\frac {3840}{\left (\ln \left (4 x \right )-19\right )^{2} \left (x -1\right )}\)	\(16\)
risch	\(-\frac {3840}{\left (\ln \left (4 x \right )-19\right )^{2} \left (x -1\right )}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3840*x*ln(4*x)-65280*x-7680)/((x^3-2*x^2+x)*ln(4*x)^3+(-57*x^3+114*x^2-57*x)*ln(4*x)^2+(1083*x^3-2166*x^2
+1083*x)*ln(4*x)-6859*x^3+13718*x^2-6859*x),x,method=_RETURNVERBOSE)

[Out]

-3840/(ln(4*x)-19)^2/(x-1)

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maxima [B]  time = 0.49, size = 56, normalized size = 3.29 \begin {gather*} -\frac {3840}{{\left (x - 1\right )} \log \relax (x)^{2} + {\left (4 \, \log \relax (2)^{2} - 76 \, \log \relax (2) + 361\right )} x - 4 \, \log \relax (2)^{2} + 2 \, {\left (x {\left (2 \, \log \relax (2) - 19\right )} - 2 \, \log \relax (2) + 19\right )} \log \relax (x) + 76 \, \log \relax (2) - 361} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3840*x*log(4*x)-65280*x-7680)/((x^3-2*x^2+x)*log(4*x)^3+(-57*x^3+114*x^2-57*x)*log(4*x)^2+(1083*x^3
-2166*x^2+1083*x)*log(4*x)-6859*x^3+13718*x^2-6859*x),x, algorithm="maxima")

[Out]

-3840/((x - 1)*log(x)^2 + (4*log(2)^2 - 76*log(2) + 361)*x - 4*log(2)^2 + 2*(x*(2*log(2) - 19) - 2*log(2) + 19
)*log(x) + 76*log(2) - 361)

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mupad [B]  time = 3.85, size = 42, normalized size = 2.47 \begin {gather*} -\frac {\frac {3840\,{\ln \left (4\,x\right )}^2}{361}-\frac {7680\,\ln \left (4\,x\right )}{19}+3840}{{\left (\ln \left (4\,x\right )-19\right )}^2}-\frac {3840}{{\left (\ln \left (4\,x\right )-19\right )}^2\,\left (x-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((65280*x - 3840*x*log(4*x) + 7680)/(6859*x - log(4*x)*(1083*x - 2166*x^2 + 1083*x^3) + log(4*x)^2*(57*x -
114*x^2 + 57*x^3) - 13718*x^2 + 6859*x^3 - log(4*x)^3*(x - 2*x^2 + x^3)),x)

[Out]

- ((3840*log(4*x)^2)/361 - (7680*log(4*x))/19 + 3840)/(log(4*x) - 19)^2 - 3840/((log(4*x) - 19)^2*(x - 1))

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sympy [B]  time = 0.16, size = 27, normalized size = 1.59 \begin {gather*} - \frac {3840}{361 x + \left (38 - 38 x\right ) \log {\left (4 x \right )} + \left (x - 1\right ) \log {\left (4 x \right )}^{2} - 361} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3840*x*ln(4*x)-65280*x-7680)/((x**3-2*x**2+x)*ln(4*x)**3+(-57*x**3+114*x**2-57*x)*ln(4*x)**2+(1083*
x**3-2166*x**2+1083*x)*ln(4*x)-6859*x**3+13718*x**2-6859*x),x)

[Out]

-3840/(361*x + (38 - 38*x)*log(4*x) + (x - 1)*log(4*x)**2 - 361)

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