3.41.61 \(\int \frac {288+504 x+16 x^2}{-144 x-504 x^2-437 x^3+16 x^3 \log (x)} \, dx\)

Optimal. Leaf size=20 \[ \log \left (-\frac {1}{4}+\left (-\frac {21}{4}-\frac {3}{x}\right )^2-\log (x)\right ) \]

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Rubi [F]  time = 0.25, 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 {288+504 x+16 x^2}{-144 x-504 x^2-437 x^3+16 x^3 \log (x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(288 + 504*x + 16*x^2)/(-144*x - 504*x^2 - 437*x^3 + 16*x^3*Log[x]),x]

[Out]

504*Defer[Int][(-144 - 504*x - 437*x^2 + 16*x^2*Log[x])^(-1), x] + 288*Defer[Int][1/(x*(-144 - 504*x - 437*x^2
+ 16*x^2*Log[x])), x] + 16*Defer[Int][x/(-144 - 504*x - 437*x^2 + 16*x^2*Log[x]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {504}{-144-504 x-437 x^2+16 x^2 \log (x)}+\frac {288}{x \left (-144-504 x-437 x^2+16 x^2 \log (x)\right )}+\frac {16 x}{-144-504 x-437 x^2+16 x^2 \log (x)}\right ) \, dx\\ &=16 \int \frac {x}{-144-504 x-437 x^2+16 x^2 \log (x)} \, dx+288 \int \frac {1}{x \left (-144-504 x-437 x^2+16 x^2 \log (x)\right )} \, dx+504 \int \frac {1}{-144-504 x-437 x^2+16 x^2 \log (x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.12, size = 31, normalized size = 1.55 \begin {gather*} 8 \left (-\frac {\log (x)}{4}+\frac {1}{8} \log \left (144+504 x+437 x^2-16 x^2 \log (x)\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(288 + 504*x + 16*x^2)/(-144*x - 504*x^2 - 437*x^3 + 16*x^3*Log[x]),x]

[Out]

8*(-1/4*Log[x] + Log[144 + 504*x + 437*x^2 - 16*x^2*Log[x]]/8)

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fricas [A]  time = 0.51, size = 22, normalized size = 1.10 \begin {gather*} \log \left (\frac {16 \, x^{2} \log \relax (x) - 437 \, x^{2} - 504 \, x - 144}{x^{2}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x^2+504*x+288)/(16*x^3*log(x)-437*x^3-504*x^2-144*x),x, algorithm="fricas")

[Out]

log((16*x^2*log(x) - 437*x^2 - 504*x - 144)/x^2)

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giac [A]  time = 0.17, size = 23, normalized size = 1.15 \begin {gather*} \log \left (16 \, x^{2} \log \relax (x) - 437 \, x^{2} - 504 \, x - 144\right ) - 2 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x^2+504*x+288)/(16*x^3*log(x)-437*x^3-504*x^2-144*x),x, algorithm="giac")

[Out]

log(16*x^2*log(x) - 437*x^2 - 504*x - 144) - 2*log(x)

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maple [A]  time = 0.02, size = 20, normalized size = 1.00

method	result	size
risch	\(\ln \left (\ln \relax (x )-\frac {437 x^{2}+504 x +144}{16 x^{2}}\right )\)	\(20\)
norman	\(-2 \ln \relax (x )+\ln \left (16 x^{2} \ln \relax (x )-437 x^{2}-504 x -144\right )\)	\(24\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((16*x^2+504*x+288)/(16*x^3*ln(x)-437*x^3-504*x^2-144*x),x,method=_RETURNVERBOSE)

[Out]

ln(ln(x)-1/16*(437*x^2+504*x+144)/x^2)

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maxima [A]  time = 0.40, size = 23, normalized size = 1.15 \begin {gather*} \log \left (\frac {16 \, x^{2} \log \relax (x) - 437 \, x^{2} - 504 \, x - 144}{16 \, x^{2}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x^2+504*x+288)/(16*x^3*log(x)-437*x^3-504*x^2-144*x),x, algorithm="maxima")

[Out]

log(1/16*(16*x^2*log(x) - 437*x^2 - 504*x - 144)/x^2)

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mupad [B]  time = 3.21, size = 23, normalized size = 1.15 \begin {gather*} \ln \left (504\,x-16\,x^2\,\ln \relax (x)+437\,x^2+144\right )-2\,\ln \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(504*x + 16*x^2 + 288)/(144*x - 16*x^3*log(x) + 504*x^2 + 437*x^3),x)

[Out]

log(504*x - 16*x^2*log(x) + 437*x^2 + 144) - 2*log(x)

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sympy [A]  time = 0.18, size = 20, normalized size = 1.00 \begin {gather*} \log {\left (\log {\relax (x )} + \frac {- 437 x^{2} - 504 x - 144}{16 x^{2}} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x**2+504*x+288)/(16*x**3*ln(x)-437*x**3-504*x**2-144*x),x)

[Out]

log(log(x) + (-437*x**2 - 504*x - 144)/(16*x**2))

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