3.104.13 \(\int \frac {87+3 x-87 x^2-3 x^3+(-87-6 x-87 x^2) \log (x)}{(1-2 x^2+x^4) \log ^2(x)} \, dx\)

Optimal. Leaf size=18 \[ \frac {3 (29+x)}{\left (-\frac {1}{x}+x\right ) \log (x)} \]

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Rubi [F]  time = 0.23, 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 {87+3 x-87 x^2-3 x^3+\left (-87-6 x-87 x^2\right ) \log (x)}{\left (1-2 x^2+x^4\right ) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(87 + 3*x - 87*x^2 - 3*x^3 + (-87 - 6*x - 87*x^2)*Log[x])/((1 - 2*x^2 + x^4)*Log[x]^2),x]

[Out]

-3*Defer[Int][(29 + x)/((-1 + x^2)*Log[x]^2), x] - 3*Defer[Int][(29 + 2*x + 29*x^2)/((-1 + x^2)^2*Log[x]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {87+3 x-87 x^2-3 x^3+\left (-87-6 x-87 x^2\right ) \log (x)}{\left (-1+x^2\right )^2 \log ^2(x)} \, dx\\ &=\int \left (-\frac {3 (29+x)}{\left (-1+x^2\right ) \log ^2(x)}-\frac {3 \left (29+2 x+29 x^2\right )}{\left (-1+x^2\right )^2 \log (x)}\right ) \, dx\\ &=-\left (3 \int \frac {29+x}{\left (-1+x^2\right ) \log ^2(x)} \, dx\right )-3 \int \frac {29+2 x+29 x^2}{\left (-1+x^2\right )^2 \log (x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.08, size = 17, normalized size = 0.94 \begin {gather*} \frac {3 x (29+x)}{\left (-1+x^2\right ) \log (x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(87 + 3*x - 87*x^2 - 3*x^3 + (-87 - 6*x - 87*x^2)*Log[x])/((1 - 2*x^2 + x^4)*Log[x]^2),x]

[Out]

(3*x*(29 + x))/((-1 + x^2)*Log[x])

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fricas [A]  time = 1.23, size = 20, normalized size = 1.11 \begin {gather*} \frac {3 \, {\left (x^{2} + 29 \, x\right )}}{{\left (x^{2} - 1\right )} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-87*x^2-6*x-87)*log(x)-3*x^3-87*x^2+3*x+87)/(x^4-2*x^2+1)/log(x)^2,x, algorithm="fricas")

[Out]

3*(x^2 + 29*x)/((x^2 - 1)*log(x))

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giac [A]  time = 0.16, size = 22, normalized size = 1.22 \begin {gather*} \frac {3 \, {\left (x^{2} + 29 \, x\right )}}{x^{2} \log \relax (x) - \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-87*x^2-6*x-87)*log(x)-3*x^3-87*x^2+3*x+87)/(x^4-2*x^2+1)/log(x)^2,x, algorithm="giac")

[Out]

3*(x^2 + 29*x)/(x^2*log(x) - log(x))

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maple [A]  time = 0.06, size = 18, normalized size = 1.00

method	result	size
risch	\(\frac {3 x \left (x +29\right )}{\left (x^{2}-1\right ) \ln \relax (x )}\)	\(18\)
norman	\(\frac {3 x^{2}+87 x}{\left (x^{2}-1\right ) \ln \relax (x )}\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-87*x^2-6*x-87)*ln(x)-3*x^3-87*x^2+3*x+87)/(x^4-2*x^2+1)/ln(x)^2,x,method=_RETURNVERBOSE)

[Out]

3*x*(x+29)/(x^2-1)/ln(x)

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maxima [A]  time = 0.38, size = 20, normalized size = 1.11 \begin {gather*} \frac {3 \, {\left (x^{2} + 29 \, x\right )}}{{\left (x^{2} - 1\right )} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-87*x^2-6*x-87)*log(x)-3*x^3-87*x^2+3*x+87)/(x^4-2*x^2+1)/log(x)^2,x, algorithm="maxima")

[Out]

3*(x^2 + 29*x)/((x^2 - 1)*log(x))

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mupad [B]  time = 8.56, size = 17, normalized size = 0.94 \begin {gather*} \frac {3\,x\,\left (x+29\right )}{\ln \relax (x)\,\left (x^2-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x)*(6*x + 87*x^2 + 87) - 3*x + 87*x^2 + 3*x^3 - 87)/(log(x)^2*(x^4 - 2*x^2 + 1)),x)

[Out]

(3*x*(x + 29))/(log(x)*(x^2 - 1))

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sympy [A]  time = 0.12, size = 15, normalized size = 0.83 \begin {gather*} \frac {3 x^{2} + 87 x}{\left (x^{2} - 1\right ) \log {\relax (x )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-87*x**2-6*x-87)*ln(x)-3*x**3-87*x**2+3*x+87)/(x**4-2*x**2+1)/ln(x)**2,x)

[Out]

(3*x**2 + 87*x)/((x**2 - 1)*log(x))

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