3.76.82 \(\int \frac {-72+4 e^5}{e^3} \, dx\)

Optimal. Leaf size=12 \[ 4 \left (-\frac {18}{e^3}+e^2\right ) x \]

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Rubi [A]  time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.08, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {8} \begin {gather*} -\frac {4 \left (18-e^5\right ) x}{e^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-72 + 4*E^5)/E^3,x]

[Out]

(-4*(18 - E^5)*x)/E^3

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {4 \left (18-e^5\right ) x}{e^3}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 1.08 \begin {gather*} -\frac {72 x}{e^3}+4 e^2 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-72 + 4*E^5)/E^3,x]

[Out]

(-72*x)/E^3 + 4*E^2*x

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fricas [A]  time = 0.70, size = 12, normalized size = 1.00 \begin {gather*} 4 \, {\left (x e^{5} - 18 \, x\right )} e^{\left (-3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*exp(2)*exp(3)-72)/exp(3),x, algorithm="fricas")

[Out]

4*(x*e^5 - 18*x)*e^(-3)

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giac [A]  time = 0.12, size = 9, normalized size = 0.75 \begin {gather*} 4 \, x {\left (e^{5} - 18\right )} e^{\left (-3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*exp(2)*exp(3)-72)/exp(3),x, algorithm="giac")

[Out]

4*x*(e^5 - 18)*e^(-3)

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maple [A]  time = 0.02, size = 14, normalized size = 1.17

method	result	size
risch	\(4 \,{\mathrm e}^{-3} x \,{\mathrm e}^{5}-72 \,{\mathrm e}^{-3} x\)	\(14\)
default	\(\left (4 \,{\mathrm e}^{2} {\mathrm e}^{3}-72\right ) {\mathrm e}^{-3} x\)	\(15\)
norman	\(4 \left ({\mathrm e}^{2} {\mathrm e}^{3}-18\right ) {\mathrm e}^{-3} x\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*exp(2)*exp(3)-72)/exp(3),x,method=_RETURNVERBOSE)

[Out]

4*exp(-3)*x*exp(5)-72*exp(-3)*x

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maxima [A]  time = 0.47, size = 9, normalized size = 0.75 \begin {gather*} 4 \, x {\left (e^{5} - 18\right )} e^{\left (-3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*exp(2)*exp(3)-72)/exp(3),x, algorithm="maxima")

[Out]

4*x*(e^5 - 18)*e^(-3)

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mupad [B]  time = 0.00, size = 10, normalized size = 0.83 \begin {gather*} x\,{\mathrm {e}}^{-3}\,\left (4\,{\mathrm {e}}^5-72\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-3)*(4*exp(5) - 72),x)

[Out]

x*exp(-3)*(4*exp(5) - 72)

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sympy [A]  time = 0.04, size = 10, normalized size = 0.83 \begin {gather*} \frac {x \left (-72 + 4 e^{5}\right )}{e^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*exp(2)*exp(3)-72)/exp(3),x)

[Out]

x*(-72 + 4*exp(5))*exp(-3)

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