3.85.70 \(\int (-108+12 e^{16}) \, dx\)

Optimal. Leaf size=16 \[ -24 \left (4+\frac {1}{2} \left (1-e^{16}\right )\right ) x \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.62, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {8} \begin {gather*} -12 \left (9-e^{16}\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-108 + 12*E^16,x]

[Out]

-12*(9 - E^16)*x

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-12 \left (9-e^{16}\right ) x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.62 \begin {gather*} -108 x+12 e^{16} x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-108 + 12*E^16,x]

[Out]

-108*x + 12*E^16*x

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fricas [A]  time = 0.65, size = 9, normalized size = 0.56 \begin {gather*} 12 \, x e^{16} - 108 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(12*exp(16)-108,x, algorithm="fricas")

[Out]

12*x*e^16 - 108*x

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giac [A]  time = 0.24, size = 7, normalized size = 0.44 \begin {gather*} 12 \, x {\left (e^{16} - 9\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(12*exp(16)-108,x, algorithm="giac")

[Out]

12*x*(e^16 - 9)

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maple [A]  time = 0.01, size = 9, normalized size = 0.56

method	result	size
default	\(\left (12 \,{\mathrm e}^{16}-108\right ) x\)	\(9\)
norman	\(\left (12 \,{\mathrm e}^{16}-108\right ) x\)	\(9\)
risch	\(12 x \,{\mathrm e}^{16}-108 x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(12*exp(16)-108,x,method=_RETURNVERBOSE)

[Out]

(12*exp(16)-108)*x

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maxima [A]  time = 0.41, size = 7, normalized size = 0.44 \begin {gather*} 12 \, x {\left (e^{16} - 9\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(12*exp(16)-108,x, algorithm="maxima")

[Out]

12*x*(e^16 - 9)

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mupad [B]  time = 0.00, size = 8, normalized size = 0.50 \begin {gather*} x\,\left (12\,{\mathrm {e}}^{16}-108\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(12*exp(16) - 108,x)

[Out]

x*(12*exp(16) - 108)

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sympy [A]  time = 0.04, size = 7, normalized size = 0.44 \begin {gather*} x \left (-108 + 12 e^{16}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(12*exp(16)-108,x)

[Out]

x*(-108 + 12*exp(16))

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