3.50.49 \(\int \frac {4-27 x-8 x^2-16 x^4}{x} \, dx\)

Optimal. Leaf size=19 \[ x-4 \left (-6+7 x+x^2+x^4-\log (x)\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {14} \begin {gather*} -4 x^4-4 x^2-27 x+4 \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(4 - 27*x - 8*x^2 - 16*x^4)/x,x]

[Out]

-27*x - 4*x^2 - 4*x^4 + 4*Log[x]

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-27+\frac {4}{x}-8 x-16 x^3\right ) \, dx\\ &=-27 x-4 x^2-4 x^4+4 \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 18, normalized size = 0.95 \begin {gather*} -27 x-4 x^2-4 x^4+4 \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(4 - 27*x - 8*x^2 - 16*x^4)/x,x]

[Out]

-27*x - 4*x^2 - 4*x^4 + 4*Log[x]

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fricas [A]  time = 0.90, size = 18, normalized size = 0.95 \begin {gather*} -4 \, x^{4} - 4 \, x^{2} - 27 \, x + 4 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-16*x^4-8*x^2-27*x+4)/x,x, algorithm="fricas")

[Out]

-4*x^4 - 4*x^2 - 27*x + 4*log(x)

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giac [A]  time = 0.20, size = 19, normalized size = 1.00 \begin {gather*} -4 \, x^{4} - 4 \, x^{2} - 27 \, x + 4 \, \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-16*x^4-8*x^2-27*x+4)/x,x, algorithm="giac")

[Out]

-4*x^4 - 4*x^2 - 27*x + 4*log(abs(x))

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maple [A]  time = 0.02, size = 19, normalized size = 1.00

method	result	size
default	\(-4 x^{4}-4 x^{2}-27 x +4 \ln \relax (x )\)	\(19\)
norman	\(-4 x^{4}-4 x^{2}-27 x +4 \ln \relax (x )\)	\(19\)
risch	\(-4 x^{4}-4 x^{2}-27 x +4 \ln \relax (x )\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-16*x^4-8*x^2-27*x+4)/x,x,method=_RETURNVERBOSE)

[Out]

-4*x^4-4*x^2-27*x+4*ln(x)

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maxima [A]  time = 0.56, size = 18, normalized size = 0.95 \begin {gather*} -4 \, x^{4} - 4 \, x^{2} - 27 \, x + 4 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-16*x^4-8*x^2-27*x+4)/x,x, algorithm="maxima")

[Out]

-4*x^4 - 4*x^2 - 27*x + 4*log(x)

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mupad [B]  time = 0.03, size = 18, normalized size = 0.95 \begin {gather*} 4\,\ln \relax (x)-27\,x-4\,x^2-4\,x^4 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(27*x + 8*x^2 + 16*x^4 - 4)/x,x)

[Out]

4*log(x) - 27*x - 4*x^2 - 4*x^4

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sympy [A]  time = 0.07, size = 17, normalized size = 0.89 \begin {gather*} - 4 x^{4} - 4 x^{2} - 27 x + 4 \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-16*x**4-8*x**2-27*x+4)/x,x)

[Out]

-4*x**4 - 4*x**2 - 27*x + 4*log(x)

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