\(\int (-6+e^{5 x-x^3} (-20+12 x^2)-\log (x)) \, dx\) [9877]

Optimal result

Integrand size = 25, antiderivative size = 26 \[ \int \left (-6+e^{5 x-x^3} \left (-20+12 x^2\right )-\log (x)\right ) \, dx=-4 e^{\left (\frac {5}{x}-x\right ) x^2}-5 x-x \log (x) \]

[Out]

-4*exp(x^2*(5/x-x))-x*ln(x)-5*x

Rubi [A] (verified)

Time = 0.03 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.85, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {6838, 2332} \[ \int \left (-6+e^{5 x-x^3} \left (-20+12 x^2\right )-\log (x)\right ) \, dx=-4 e^{5 x-x^3}-5 x+x (-\log (x)) \]

[In]

Int[-6 + E^(5*x - x^3)*(-20 + 12*x^2) - Log[x],x]

[Out]

-4*E^(5*x - x^3) - 5*x - x*Log[x]

Rule 2332

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

Rule 6838

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[q*(F^v/Log[F]), x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps \begin{align*} \text {integral}& = -6 x+\int e^{5 x-x^3} \left (-20+12 x^2\right ) \, dx-\int \log (x) \, dx \\ & = -4 e^{5 x-x^3}-5 x-x \log (x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.05 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.85 \[ \int \left (-6+e^{5 x-x^3} \left (-20+12 x^2\right )-\log (x)\right ) \, dx=-4 e^{5 x-x^3}-5 x-x \log (x) \]

[In]

Integrate[-6 + E^(5*x - x^3)*(-20 + 12*x^2) - Log[x],x]

[Out]

-4*E^(5*x - x^3) - 5*x - x*Log[x]

Maple [A] (verified)

Time = 0.07 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.81

method	result	size
risch	\(-5 x -4 \,{\mathrm e}^{-x \left (x^{2}-5\right )}-x \ln \left (x \right )\)	\(21\)
default	\(-5 x -4 \,{\mathrm e}^{-x^{3}+5 x}-x \ln \left (x \right )\)	\(22\)
norman	\(-5 x -4 \,{\mathrm e}^{-x^{3}+5 x}-x \ln \left (x \right )\)	\(22\)
parallelrisch	\(-5 x -4 \,{\mathrm e}^{-x^{3}+5 x}-x \ln \left (x \right )\)	\(22\)
parts	\(-5 x -4 \,{\mathrm e}^{-x^{3}+5 x}-x \ln \left (x \right )\)	\(22\)

[In]

int(-ln(x)+(12*x^2-20)*exp(-x^3+5*x)-6,x,method=_RETURNVERBOSE)

[Out]

-5*x-4*exp(-x*(x^2-5))-x*ln(x)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.81 \[ \int \left (-6+e^{5 x-x^3} \left (-20+12 x^2\right )-\log (x)\right ) \, dx=-x \log \left (x\right ) - 5 \, x - 4 \, e^{\left (-x^{3} + 5 \, x\right )} \]

[In]

integrate(-log(x)+(12*x^2-20)*exp(-x^3+5*x)-6,x, algorithm="fricas")

[Out]

-x*log(x) - 5*x - 4*e^(-x^3 + 5*x)

Sympy [A] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.73 \[ \int \left (-6+e^{5 x-x^3} \left (-20+12 x^2\right )-\log (x)\right ) \, dx=- x \log {\left (x \right )} - 5 x - 4 e^{- x^{3} + 5 x} \]

[In]

integrate(-ln(x)+(12*x**2-20)*exp(-x**3+5*x)-6,x)

[Out]

-x*log(x) - 5*x - 4*exp(-x**3 + 5*x)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.81 \[ \int \left (-6+e^{5 x-x^3} \left (-20+12 x^2\right )-\log (x)\right ) \, dx=-x \log \left (x\right ) - 5 \, x - 4 \, e^{\left (-x^{3} + 5 \, x\right )} \]

[In]

integrate(-log(x)+(12*x^2-20)*exp(-x^3+5*x)-6,x, algorithm="maxima")

[Out]

-x*log(x) - 5*x - 4*e^(-x^3 + 5*x)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.81 \[ \int \left (-6+e^{5 x-x^3} \left (-20+12 x^2\right )-\log (x)\right ) \, dx=-x \log \left (x\right ) - 5 \, x - 4 \, e^{\left (-x^{3} + 5 \, x\right )} \]

[In]

integrate(-log(x)+(12*x^2-20)*exp(-x^3+5*x)-6,x, algorithm="giac")

[Out]

-x*log(x) - 5*x - 4*e^(-x^3 + 5*x)

Mupad [B] (verification not implemented)

Time = 18.23 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.81 \[ \int \left (-6+e^{5 x-x^3} \left (-20+12 x^2\right )-\log (x)\right ) \, dx=-5\,x-4\,{\mathrm {e}}^{5\,x-x^3}-x\,\ln \left (x\right ) \]

[In]

int(exp(5*x - x^3)*(12*x^2 - 20) - log(x) - 6,x)

[Out]

- 5*x - 4*exp(5*x - x^3) - x*log(x)