3.72.1 \(\int \frac {42-6 e^6+6 x^2+24 \log (3)}{x^2} \, dx\)

Optimal. Leaf size=19 \[ \frac {6 \left (-7+e^6+x (4+x)-4 \log (3)\right )}{x} \]

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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 = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {14} \begin {gather*} 6 x-\frac {6 \left (7-e^6+\log (81)\right )}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(42 - 6*E^6 + 6*x^2 + 24*Log[3])/x^2,x]

[Out]

6*x - (6*(7 - E^6 + Log[81]))/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 (6-\frac {6 \left (-7+e^6-4 \log (3)\right )}{x^2}\right ) \, dx\\ &=6 x-\frac {6 \left (7-e^6+\log (81)\right )}{x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 17, normalized size = 0.89 \begin {gather*} 6 \left (x+\frac {-7+e^6-\log (81)}{x}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(42 - 6*E^6 + 6*x^2 + 24*Log[3])/x^2,x]

[Out]

6*(x + (-7 + E^6 - Log[81])/x)

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fricas [A]  time = 0.55, size = 16, normalized size = 0.84 \begin {gather*} \frac {6 \, {\left (x^{2} + e^{6} - 4 \, \log \relax (3) - 7\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*log(3)-6*exp(3)^2+6*x^2+42)/x^2,x, algorithm="fricas")

[Out]

6*(x^2 + e^6 - 4*log(3) - 7)/x

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giac [A]  time = 0.14, size = 17, normalized size = 0.89 \begin {gather*} 6 \, x + \frac {6 \, {\left (e^{6} - 4 \, \log \relax (3) - 7\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*log(3)-6*exp(3)^2+6*x^2+42)/x^2,x, algorithm="giac")

[Out]

6*x + 6*(e^6 - 4*log(3) - 7)/x

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maple [A]  time = 0.03, size = 19, normalized size = 1.00

method	result	size
gosper	\(\frac {6 \,{\mathrm e}^{6}+6 x^{2}-24 \ln \relax (3)-42}{x}\)	\(19\)
default	\(6 x -\frac {6 \left (4 \ln \relax (3)-{\mathrm e}^{6}+7\right )}{x}\)	\(20\)
norman	\(\frac {6 \,{\mathrm e}^{6}+6 x^{2}-24 \ln \relax (3)-42}{x}\)	\(22\)
risch	\(6 x +\frac {6 \,{\mathrm e}^{6}}{x}-\frac {24 \ln \relax (3)}{x}-\frac {42}{x}\)	\(24\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((24*ln(3)-6*exp(3)^2+6*x^2+42)/x^2,x,method=_RETURNVERBOSE)

[Out]

6*(exp(3)^2+x^2-4*ln(3)-7)/x

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maxima [A]  time = 0.37, size = 17, normalized size = 0.89 \begin {gather*} 6 \, x + \frac {6 \, {\left (e^{6} - 4 \, \log \relax (3) - 7\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*log(3)-6*exp(3)^2+6*x^2+42)/x^2,x, algorithm="maxima")

[Out]

6*x + 6*(e^6 - 4*log(3) - 7)/x

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mupad [B]  time = 0.04, size = 19, normalized size = 1.00 \begin {gather*} 6\,x-\frac {24\,\ln \relax (3)-6\,{\mathrm {e}}^6+42}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((24*log(3) - 6*exp(6) + 6*x^2 + 42)/x^2,x)

[Out]

6*x - (24*log(3) - 6*exp(6) + 42)/x

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sympy [A]  time = 0.12, size = 15, normalized size = 0.79 \begin {gather*} 6 x + \frac {-42 - 24 \log {\relax (3 )} + 6 e^{6}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*ln(3)-6*exp(3)**2+6*x**2+42)/x**2,x)

[Out]

6*x + (-42 - 24*log(3) + 6*exp(6))/x

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