\(\int \frac {2 x^3-2 \log (3)}{x^3} \, dx\) [6609]

Optimal result

Integrand size = 14, antiderivative size = 16 \[ \int \frac {2 x^3-2 \log (3)}{x^3} \, dx=-1-e^2+2 x+\frac {\log (3)}{x^2} \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {14} \[ \int \frac {2 x^3-2 \log (3)}{x^3} \, dx=\frac {\log (9)}{2 x^2}+2 x \]

[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{align*} \text {integral}& = \int \left (2-\frac {\log (9)}{x^3}\right ) \, dx \\ & = 2 x+\frac {\log (9)}{2 x^2} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81 \[ \int \frac {2 x^3-2 \log (3)}{x^3} \, dx=2 x+\frac {\log (9)}{2 x^2} \]

[In]

Integrate[(2*x^3 - 2*Log[3])/x^3,x]

[Out]

2*x + Log[9]/(2*x^2)

Maple [A] (verified)

Time = 0.09 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.69

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

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \frac {2 x^3-2 \log (3)}{x^3} \, dx=\frac {2 \, x^{3} + \log \left (3\right )}{x^{2}} \]

[In]

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

[Out]

(2*x^3 + log(3))/x^2

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.50 \[ \int \frac {2 x^3-2 \log (3)}{x^3} \, dx=2 x + \frac {\log {\left (3 \right )}}{x^{2}} \]

[In]

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

[Out]

2*x + log(3)/x**2

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.62 \[ \int \frac {2 x^3-2 \log (3)}{x^3} \, dx=2 \, x + \frac {\log \left (3\right )}{x^{2}} \]

[In]

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

[Out]

2*x + log(3)/x^2

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.62 \[ \int \frac {2 x^3-2 \log (3)}{x^3} \, dx=2 \, x + \frac {\log \left (3\right )}{x^{2}} \]

[In]

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

[Out]

2*x + log(3)/x^2

Mupad [B] (verification not implemented)

Time = 11.06 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.62 \[ \int \frac {2 x^3-2 \log (3)}{x^3} \, dx=2\,x+\frac {\ln \left (3\right )}{x^2} \]

[In]

int(-(2*log(3) - 2*x^3)/x^3,x)

[Out]

2*x + log(3)/x^2