3.67.9 \(\int \frac {2 x^3-2 \log (3)}{x^3} \, dx\)

Optimal. Leaf size=16 \[ -1-e^2+2 x+\frac {\log (3)}{x^2} \]

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Rubi [A]  time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.81, number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {14} \begin {gather*} \frac {\log (9)}{2 x^2}+2 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(2*x^3 - 2*Log[3])/x^3,x]

[Out]

2*x + Log[9]/(2*x^2)

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

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Mathematica [A]  time = 0.00, size = 13, normalized size = 0.81 \begin {gather*} 2 x+\frac {\log (9)}{2 x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(2*x^3 - 2*Log[3])/x^3,x]

[Out]

2*x + Log[9]/(2*x^2)

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fricas [A]  time = 0.58, size = 12, normalized size = 0.75 \begin {gather*} \frac {2 \, x^{3} + \log \relax (3)}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(2*x^3 + log(3))/x^2

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giac [A]  time = 0.14, size = 10, normalized size = 0.62 \begin {gather*} 2 \, x + \frac {\log \relax (3)}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*x + log(3)/x^2

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maple [A]  time = 0.06, size = 11, normalized size = 0.69

method	result	size
default	\(2 x +\frac {\ln \relax (3)}{x^{2}}\)	\(11\)
risch	\(2 x +\frac {\ln \relax (3)}{x^{2}}\)	\(11\)
gosper	\(\frac {2 x^{3}+\ln \relax (3)}{x^{2}}\)	\(13\)
norman	\(\frac {2 x^{3}+\ln \relax (3)}{x^{2}}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*x+1/x^2*ln(3)

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maxima [A]  time = 0.37, size = 10, normalized size = 0.62 \begin {gather*} 2 \, x + \frac {\log \relax (3)}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*x + log(3)/x^2

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mupad [B]  time = 4.26, size = 10, normalized size = 0.62 \begin {gather*} 2\,x+\frac {\ln \relax (3)}{x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*log(3) - 2*x^3)/x^3,x)

[Out]

2*x + log(3)/x^2

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sympy [A]  time = 0.08, size = 8, normalized size = 0.50 \begin {gather*} 2 x + \frac {\log {\relax (3 )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2*ln(3)+2*x**3)/x**3,x)

[Out]

2*x + log(3)/x**2

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