3.24.8 \(\int \frac {1-7 x+2 x^2}{(16 x-7 x^2+x^3+x \log (8 x)) \log (16-7 x+x^2+\log (8 x))} \, dx\)

Optimal. Leaf size=13 \[ \log \left (\log \left ((-4+x)^2+x+\log (8 x)\right )\right ) \]

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Rubi [A]  time = 0.09, antiderivative size = 14, normalized size of antiderivative = 1.08, number of steps used = 1, number of rules used = 1, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.022, Rules used = {6684} \begin {gather*} \log \left (\log \left (x^2-7 x+\log (8 x)+16\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 - 7*x + 2*x^2)/((16*x - 7*x^2 + x^3 + x*Log[8*x])*Log[16 - 7*x + x^2 + Log[8*x]]),x]

[Out]

Log[Log[16 - 7*x + x^2 + Log[8*x]]]

Rule 6684

Int[(u_)/(y_), x_Symbol] :> With[{q = DerivativeDivides[y, u, x]}, Simp[q*Log[RemoveContent[y, x]], x] /;  !Fa
lseQ[q]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\log \left (\log \left (16-7 x+x^2+\log (8 x)\right )\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.23, size = 14, normalized size = 1.08 \begin {gather*} \log \left (\log \left (16-7 x+x^2+\log (8 x)\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - 7*x + 2*x^2)/((16*x - 7*x^2 + x^3 + x*Log[8*x])*Log[16 - 7*x + x^2 + Log[8*x]]),x]

[Out]

Log[Log[16 - 7*x + x^2 + Log[8*x]]]

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fricas [A]  time = 0.89, size = 14, normalized size = 1.08 \begin {gather*} \log \left (\log \left (x^{2} - 7 \, x + \log \left (8 \, x\right ) + 16\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x^2-7*x+1)/(x*log(8*x)+x^3-7*x^2+16*x)/log(log(8*x)+x^2-7*x+16),x, algorithm="fricas")

[Out]

log(log(x^2 - 7*x + log(8*x) + 16))

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giac [A]  time = 0.24, size = 14, normalized size = 1.08 \begin {gather*} \log \left (\log \left (x^{2} - 7 \, x + \log \left (8 \, x\right ) + 16\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x^2-7*x+1)/(x*log(8*x)+x^3-7*x^2+16*x)/log(log(8*x)+x^2-7*x+16),x, algorithm="giac")

[Out]

log(log(x^2 - 7*x + log(8*x) + 16))

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maple [A]  time = 0.04, size = 15, normalized size = 1.15

method	result	size
risch	\(\ln \left (\ln \left (\ln \left (8 x \right )+x^{2}-7 x +16\right )\right )\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x^2-7*x+1)/(x*ln(8*x)+x^3-7*x^2+16*x)/ln(ln(8*x)+x^2-7*x+16),x,method=_RETURNVERBOSE)

[Out]

ln(ln(ln(8*x)+x^2-7*x+16))

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maxima [A]  time = 0.97, size = 16, normalized size = 1.23 \begin {gather*} \log \left (\log \left (x^{2} - 7 \, x + 3 \, \log \relax (2) + \log \relax (x) + 16\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x^2-7*x+1)/(x*log(8*x)+x^3-7*x^2+16*x)/log(log(8*x)+x^2-7*x+16),x, algorithm="maxima")

[Out]

log(log(x^2 - 7*x + 3*log(2) + log(x) + 16))

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mupad [B]  time = 1.84, size = 14, normalized size = 1.08 \begin {gather*} \ln \left (\ln \left (\ln \left (8\,x\right )-7\,x+x^2+16\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x^2 - 7*x + 1)/(log(log(8*x) - 7*x + x^2 + 16)*(16*x + x*log(8*x) - 7*x^2 + x^3)),x)

[Out]

log(log(log(8*x) - 7*x + x^2 + 16))

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sympy [A]  time = 0.46, size = 15, normalized size = 1.15 \begin {gather*} \log {\left (\log {\left (x^{2} - 7 x + \log {\left (8 x \right )} + 16 \right )} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x**2-7*x+1)/(x*ln(8*x)+x**3-7*x**2+16*x)/ln(ln(8*x)+x**2-7*x+16),x)

[Out]

log(log(x**2 - 7*x + log(8*x) + 16))

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