3.51.29 \(\int -\frac {288}{e^5} \, dx\)

Optimal. Leaf size=16 \[ 15-x^2+\left (-\frac {144}{e^5}+x\right )^2 \]

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Rubi [A]  time = 0.00, antiderivative size = 6, normalized size of antiderivative = 0.38, number of steps used = 1, number of rules used = 1, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {8} \begin {gather*} -\frac {288 x}{e^5} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-288/E^5,x]

[Out]

(-288*x)/E^5

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {288 x}{e^5}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 6, normalized size = 0.38 \begin {gather*} -\frac {288 x}{e^5} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-288/E^5,x]

[Out]

(-288*x)/E^5

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fricas [A]  time = 0.61, size = 5, normalized size = 0.31 \begin {gather*} -288 \, x e^{\left (-5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-288/exp(5),x, algorithm="fricas")

[Out]

-288*x*e^(-5)

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giac [A]  time = 0.12, size = 5, normalized size = 0.31 \begin {gather*} -288 \, x e^{\left (-5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-288/exp(5),x, algorithm="giac")

[Out]

-288*x*e^(-5)

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maple [A]  time = 0.02, size = 6, normalized size = 0.38

method	result	size
risch	\(-288 x \,{\mathrm e}^{-5}\)	\(6\)
default	\(-288 x \,{\mathrm e}^{-5}\)	\(8\)
norman	\(-288 x \,{\mathrm e}^{-5}\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-288/exp(5),x,method=_RETURNVERBOSE)

[Out]

-288*x*exp(-5)

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maxima [A]  time = 0.35, size = 5, normalized size = 0.31 \begin {gather*} -288 \, x e^{\left (-5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-288/exp(5),x, algorithm="maxima")

[Out]

-288*x*e^(-5)

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mupad [B]  time = 0.00, size = 5, normalized size = 0.31 \begin {gather*} -288\,x\,{\mathrm {e}}^{-5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-288*exp(-5),x)

[Out]

-288*x*exp(-5)

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sympy [A]  time = 0.01, size = 7, normalized size = 0.44 \begin {gather*} - \frac {288 x}{e^{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-288/exp(5),x)

[Out]

-288*x*exp(-5)

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