3.79.31 \(\int \frac {1-18 x+18 x^2-9216 x^4}{x} \, dx\)

Optimal. Leaf size=20 \[ 9 \left (x-(3-x) x-256 x^4\right )+\log (x) \]

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Rubi [A]  time = 0.00, antiderivative size = 16, normalized size of antiderivative = 0.80, 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*} -2304 x^4+9 x^2-18 x+\log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 - 18*x + 18*x^2 - 9216*x^4)/x,x]

[Out]

-18*x + 9*x^2 - 2304*x^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 (-18+\frac {1}{x}+18 x-9216 x^3\right ) \, dx\\ &=-18 x+9 x^2-2304 x^4+\log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 16, normalized size = 0.80 \begin {gather*} -18 x+9 x^2-2304 x^4+\log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - 18*x + 18*x^2 - 9216*x^4)/x,x]

[Out]

-18*x + 9*x^2 - 2304*x^4 + Log[x]

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fricas [A]  time = 0.62, size = 16, normalized size = 0.80 \begin {gather*} -2304 \, x^{4} + 9 \, x^{2} - 18 \, x + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-9216*x^4+18*x^2-18*x+1)/x,x, algorithm="fricas")

[Out]

-2304*x^4 + 9*x^2 - 18*x + log(x)

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giac [A]  time = 0.16, size = 17, normalized size = 0.85 \begin {gather*} -2304 \, x^{4} + 9 \, x^{2} - 18 \, x + \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-9216*x^4+18*x^2-18*x+1)/x,x, algorithm="giac")

[Out]

-2304*x^4 + 9*x^2 - 18*x + log(abs(x))

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maple [A]  time = 0.02, size = 17, normalized size = 0.85

method	result	size
default	\(-2304 x^{4}+9 x^{2}-18 x +\ln \relax (x )\)	\(17\)
norman	\(-2304 x^{4}+9 x^{2}-18 x +\ln \relax (x )\)	\(17\)
risch	\(-2304 x^{4}+9 x^{2}-18 x +\ln \relax (x )\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-9216*x^4+18*x^2-18*x+1)/x,x,method=_RETURNVERBOSE)

[Out]

-2304*x^4+9*x^2-18*x+ln(x)

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maxima [A]  time = 0.36, size = 16, normalized size = 0.80 \begin {gather*} -2304 \, x^{4} + 9 \, x^{2} - 18 \, x + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-9216*x^4+18*x^2-18*x+1)/x,x, algorithm="maxima")

[Out]

-2304*x^4 + 9*x^2 - 18*x + log(x)

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mupad [B]  time = 0.05, size = 16, normalized size = 0.80 \begin {gather*} \ln \relax (x)-18\,x+9\,x^2-2304\,x^4 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(18*x - 18*x^2 + 9216*x^4 - 1)/x,x)

[Out]

log(x) - 18*x + 9*x^2 - 2304*x^4

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sympy [A]  time = 0.08, size = 15, normalized size = 0.75 \begin {gather*} - 2304 x^{4} + 9 x^{2} - 18 x + \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-9216*x**4+18*x**2-18*x+1)/x,x)

[Out]

-2304*x**4 + 9*x**2 - 18*x + log(x)

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