3.15.5 \(\int \frac {-1-22 x-33 x^2-4 x^3}{x+11 x^2+11 x^3+x^4+\log (2)} \, dx\)

Optimal. Leaf size=26 \[ \log \left (\frac {2}{x \left (1+x+(10+x) \left (x+x^2\right )+\frac {\log (2)}{x}\right )}\right ) \]

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Rubi [A]  time = 0.03, antiderivative size = 20, normalized size of antiderivative = 0.77, number of steps used = 1, number of rules used = 1, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {1587} \begin {gather*} -\log \left (x^4+11 x^3+11 x^2+x+\log (2)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-1 - 22*x - 33*x^2 - 4*x^3)/(x + 11*x^2 + 11*x^3 + x^4 + Log[2]),x]

[Out]

-Log[x + 11*x^2 + 11*x^3 + x^4 + Log[2]]

Rule 1587

Int[(Pp_)/(Qq_), x_Symbol] :> With[{p = Expon[Pp, x], q = Expon[Qq, x]}, Simp[(Coeff[Pp, x, p]*Log[RemoveConte
nt[Qq, x]])/(q*Coeff[Qq, x, q]), x] /; EqQ[p, q - 1] && EqQ[Pp, Simplify[(Coeff[Pp, x, p]*D[Qq, x])/(q*Coeff[Q
q, x, q])]]] /; PolyQ[Pp, x] && PolyQ[Qq, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\log \left (x+11 x^2+11 x^3+x^4+\log (2)\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 20, normalized size = 0.77 \begin {gather*} -\log \left (x+11 x^2+11 x^3+x^4+\log (2)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1 - 22*x - 33*x^2 - 4*x^3)/(x + 11*x^2 + 11*x^3 + x^4 + Log[2]),x]

[Out]

-Log[x + 11*x^2 + 11*x^3 + x^4 + Log[2]]

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fricas [A]  time = 1.43, size = 20, normalized size = 0.77 \begin {gather*} -\log \left (x^{4} + 11 \, x^{3} + 11 \, x^{2} + x + \log \relax (2)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x^3-33*x^2-22*x-1)/(log(2)+x^4+11*x^3+11*x^2+x),x, algorithm="fricas")

[Out]

-log(x^4 + 11*x^3 + 11*x^2 + x + log(2))

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giac [A]  time = 0.30, size = 21, normalized size = 0.81 \begin {gather*} -\log \left ({\left | x^{4} + 11 \, x^{3} + 11 \, x^{2} + x + \log \relax (2) \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x^3-33*x^2-22*x-1)/(log(2)+x^4+11*x^3+11*x^2+x),x, algorithm="giac")

[Out]

-log(abs(x^4 + 11*x^3 + 11*x^2 + x + log(2)))

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maple [A]  time = 0.03, size = 21, normalized size = 0.81

method	result	size
default	\(-\ln \left (\ln \relax (2)+x^{4}+11 x^{3}+11 x^{2}+x \right )\)	\(21\)
norman	\(-\ln \left (\ln \relax (2)+x^{4}+11 x^{3}+11 x^{2}+x \right )\)	\(21\)
risch	\(-\ln \left (\ln \relax (2)+x^{4}+11 x^{3}+11 x^{2}+x \right )\)	\(21\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-4*x^3-33*x^2-22*x-1)/(ln(2)+x^4+11*x^3+11*x^2+x),x,method=_RETURNVERBOSE)

[Out]

-ln(ln(2)+x^4+11*x^3+11*x^2+x)

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maxima [A]  time = 0.55, size = 20, normalized size = 0.77 \begin {gather*} -\log \left (x^{4} + 11 \, x^{3} + 11 \, x^{2} + x + \log \relax (2)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x^3-33*x^2-22*x-1)/(log(2)+x^4+11*x^3+11*x^2+x),x, algorithm="maxima")

[Out]

-log(x^4 + 11*x^3 + 11*x^2 + x + log(2))

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mupad [B]  time = 0.07, size = 20, normalized size = 0.77 \begin {gather*} -\ln \left (x^4+11\,x^3+11\,x^2+x+\ln \relax (2)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(22*x + 33*x^2 + 4*x^3 + 1)/(x + log(2) + 11*x^2 + 11*x^3 + x^4),x)

[Out]

-log(x + log(2) + 11*x^2 + 11*x^3 + x^4)

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sympy [A]  time = 0.32, size = 20, normalized size = 0.77 \begin {gather*} - \log {\left (x^{4} + 11 x^{3} + 11 x^{2} + x + \log {\relax (2 )} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x**3-33*x**2-22*x-1)/(ln(2)+x**4+11*x**3+11*x**2+x),x)

[Out]

-log(x**4 + 11*x**3 + 11*x**2 + x + log(2))

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