\(\int (-2+\log (\frac {3 x^3}{125})) \, dx\) [3952]

Optimal result

Integrand size = 10, antiderivative size = 12 \[ \int \left (-2+\log \left (\frac {3 x^3}{125}\right )\right ) \, dx=x \left (-5+\log \left (\frac {3 x^3}{125}\right )\right ) \]

[Out]

(ln(3/125*x^3)-5)*x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2332} \[ \int \left (-2+\log \left (\frac {3 x^3}{125}\right )\right ) \, dx=x \log \left (\frac {3 x^3}{125}\right )-5 x \]

[In]

Int[-2 + Log[(3*x^3)/125],x]

[Out]

-5*x + x*Log[(3*x^3)/125]

Rule 2332

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rubi steps \begin{align*} \text {integral}& = -2 x+\int \log \left (\frac {3 x^3}{125}\right ) \, dx \\ & = -5 x+x \log \left (\frac {3 x^3}{125}\right ) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \left (-2+\log \left (\frac {3 x^3}{125}\right )\right ) \, dx=-5 x+x \log \left (\frac {3 x^3}{125}\right ) \]

[In]

Integrate[-2 + Log[(3*x^3)/125],x]

[Out]

-5*x + x*Log[(3*x^3)/125]

Maple [A] (verified)

Time = 0.19 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08

method	result	size
norman	\(x \ln \left (\frac {3 x^{3}}{125}\right )-5 x\)	\(13\)
risch	\(x \ln \left (\frac {3 x^{3}}{125}\right )-5 x\)	\(13\)
parallelrisch	\(x \ln \left (\frac {3 x^{3}}{125}\right )-5 x\)	\(13\)
default	\(-5 x -3 x \ln \left (5\right )+x \ln \left (3\right )+x \ln \left (x^{3}\right )\)	\(20\)
parts	\(-5 x -3 x \ln \left (5\right )+x \ln \left (3\right )+x \ln \left (x^{3}\right )\)	\(20\)

[In]

int(ln(3/125*x^3)-2,x,method=_RETURNVERBOSE)

[Out]

x*ln(3/125*x^3)-5*x

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \left (-2+\log \left (\frac {3 x^3}{125}\right )\right ) \, dx=x \log \left (\frac {3}{125} \, x^{3}\right ) - 5 \, x \]

[In]

integrate(log(3/125*x^3)-2,x, algorithm="fricas")

[Out]

x*log(3/125*x^3) - 5*x

Sympy [A] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \left (-2+\log \left (\frac {3 x^3}{125}\right )\right ) \, dx=x \log {\left (\frac {3 x^{3}}{125} \right )} - 5 x \]

[In]

integrate(ln(3/125*x**3)-2,x)

[Out]

x*log(3*x**3/125) - 5*x

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \left (-2+\log \left (\frac {3 x^3}{125}\right )\right ) \, dx=x \log \left (\frac {3}{125} \, x^{3}\right ) - 5 \, x \]

[In]

integrate(log(3/125*x^3)-2,x, algorithm="maxima")

[Out]

x*log(3/125*x^3) - 5*x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \left (-2+\log \left (\frac {3 x^3}{125}\right )\right ) \, dx=x \log \left (\frac {3}{125} \, x^{3}\right ) - 5 \, x \]

[In]

integrate(log(3/125*x^3)-2,x, algorithm="giac")

[Out]

x*log(3/125*x^3) - 5*x

Mupad [B] (verification not implemented)

Time = 9.99 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (-2+\log \left (\frac {3 x^3}{125}\right )\right ) \, dx=x\,\left (\ln \left (\frac {3\,x^3}{125}\right )-5\right ) \]

[In]

int(log((3*x^3)/125) - 2,x)

[Out]

x*(log((3*x^3)/125) - 5)