3.54.34 \(\int \frac {-7 x-2 x^2+3 e^3 x^3}{x} \, dx\)

Optimal. Leaf size=15 \[ e^{3 (1+\log (x))}-x (7+x) \]

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.07, number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {14} \begin {gather*} e^3 x^3-x^2-7 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-7*x - 2*x^2 + 3*E^3*x^3)/x,x]

[Out]

-7*x - x^2 + E^3*x^3

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 (-7-2 x+3 e^3 x^2\right ) \, dx\\ &=-7 x-x^2+e^3 x^3\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 16, normalized size = 1.07 \begin {gather*} -7 x-x^2+e^3 x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-7*x - 2*x^2 + 3*E^3*x^3)/x,x]

[Out]

-7*x - x^2 + E^3*x^3

________________________________________________________________________________________

fricas [A]  time = 0.58, size = 15, normalized size = 1.00 \begin {gather*} x^{3} e^{3} - x^{2} - 7 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*exp(3*log(x)+3)-2*x^2-7*x)/x,x, algorithm="fricas")

[Out]

x^3*e^3 - x^2 - 7*x

________________________________________________________________________________________

giac [A]  time = 0.20, size = 15, normalized size = 1.00 \begin {gather*} x^{3} e^{3} - x^{2} - 7 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*exp(3*log(x)+3)-2*x^2-7*x)/x,x, algorithm="giac")

[Out]

x^3*e^3 - x^2 - 7*x

________________________________________________________________________________________

maple [A]  time = 0.03, size = 16, normalized size = 1.07

method	result	size
norman	\(x^{3} {\mathrm e}^{3}-7 x -x^{2}\)	\(16\)
risch	\(x^{3} {\mathrm e}^{3}-7 x -x^{2}\)	\(16\)
default	\(-x^{2}-7 x +{\mathrm e}^{3 \ln \relax (x )+3}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*exp(3*ln(x)+3)-2*x^2-7*x)/x,x,method=_RETURNVERBOSE)

[Out]

x^3*exp(3)-7*x-x^2

________________________________________________________________________________________

maxima [A]  time = 0.43, size = 15, normalized size = 1.00 \begin {gather*} x^{3} e^{3} - x^{2} - 7 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*exp(3*log(x)+3)-2*x^2-7*x)/x,x, algorithm="maxima")

[Out]

x^3*e^3 - x^2 - 7*x

________________________________________________________________________________________

mupad [B]  time = 0.04, size = 13, normalized size = 0.87 \begin {gather*} -x\,\left (-{\mathrm {e}}^3\,x^2+x+7\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(7*x - 3*exp(3*log(x) + 3) + 2*x^2)/x,x)

[Out]

-x*(x - x^2*exp(3) + 7)

________________________________________________________________________________________

sympy [A]  time = 0.05, size = 12, normalized size = 0.80 \begin {gather*} x^{3} e^{3} - x^{2} - 7 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*exp(3*ln(x)+3)-2*x**2-7*x)/x,x)

[Out]

x**3*exp(3) - x**2 - 7*x

________________________________________________________________________________________