3.87.62 \(\int \frac {2-5 x+20 x^4 \log ^2(4)}{x} \, dx\)

Optimal. Leaf size=20 \[ 5 \left (4-x+x^4 \log ^2(4)\right )+\log \left (x^2\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 17, normalized size of antiderivative = 0.85, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {14} \begin {gather*} 5 x^4 \log ^2(4)-5 x+2 \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(2 - 5*x + 20*x^4*Log[4]^2)/x,x]

[Out]

-5*x + 5*x^4*Log[4]^2 + 2*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 (-5+\frac {2}{x}+20 x^3 \log ^2(4)\right ) \, dx\\ &=-5 x+5 x^4 \log ^2(4)+2 \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 17, normalized size = 0.85 \begin {gather*} -5 x+5 x^4 \log ^2(4)+2 \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(2 - 5*x + 20*x^4*Log[4]^2)/x,x]

[Out]

-5*x + 5*x^4*Log[4]^2 + 2*Log[x]

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fricas [A]  time = 0.50, size = 17, normalized size = 0.85 \begin {gather*} 20 \, x^{4} \log \relax (2)^{2} - 5 \, x + 2 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((80*x^4*log(2)^2-5*x+2)/x,x, algorithm="fricas")

[Out]

20*x^4*log(2)^2 - 5*x + 2*log(x)

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giac [A]  time = 0.19, size = 18, normalized size = 0.90 \begin {gather*} 20 \, x^{4} \log \relax (2)^{2} - 5 \, x + 2 \, \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((80*x^4*log(2)^2-5*x+2)/x,x, algorithm="giac")

[Out]

20*x^4*log(2)^2 - 5*x + 2*log(abs(x))

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maple [A]  time = 0.04, size = 18, normalized size = 0.90

method	result	size
default	\(-5 x +20 x^{4} \ln \relax (2)^{2}+2 \ln \relax (x )\)	\(18\)
norman	\(-5 x +20 x^{4} \ln \relax (2)^{2}+2 \ln \relax (x )\)	\(18\)
risch	\(-5 x +20 x^{4} \ln \relax (2)^{2}+2 \ln \relax (x )\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((80*x^4*ln(2)^2-5*x+2)/x,x,method=_RETURNVERBOSE)

[Out]

-5*x+20*x^4*ln(2)^2+2*ln(x)

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maxima [A]  time = 0.36, size = 17, normalized size = 0.85 \begin {gather*} 20 \, x^{4} \log \relax (2)^{2} - 5 \, x + 2 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((80*x^4*log(2)^2-5*x+2)/x,x, algorithm="maxima")

[Out]

20*x^4*log(2)^2 - 5*x + 2*log(x)

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mupad [B]  time = 0.03, size = 17, normalized size = 0.85 \begin {gather*} 2\,\ln \relax (x)-5\,x+20\,x^4\,{\ln \relax (2)}^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((80*x^4*log(2)^2 - 5*x + 2)/x,x)

[Out]

2*log(x) - 5*x + 20*x^4*log(2)^2

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sympy [A]  time = 0.08, size = 17, normalized size = 0.85 \begin {gather*} 20 x^{4} \log {\relax (2 )}^{2} - 5 x + 2 \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((80*x**4*ln(2)**2-5*x+2)/x,x)

[Out]

20*x**4*log(2)**2 - 5*x + 2*log(x)

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