3.19.73 \(\int (76-6 e^5 x) \, dx\)

Optimal. Leaf size=13 \[ x+3 x \left (25-e^5 x\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 0.92, number of steps used = 1, number of rules used = 0, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 76 x-3 e^5 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[76 - 6*E^5*x,x]

[Out]

76*x - 3*E^5*x^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=76 x-3 e^5 x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 0.92 \begin {gather*} 76 x-3 e^5 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[76 - 6*E^5*x,x]

[Out]

76*x - 3*E^5*x^2

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fricas [A]  time = 0.56, size = 11, normalized size = 0.85 \begin {gather*} -3 \, x^{2} e^{5} + 76 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-6*x*exp(5)+76,x, algorithm="fricas")

[Out]

-3*x^2*e^5 + 76*x

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giac [A]  time = 0.32, size = 11, normalized size = 0.85 \begin {gather*} -3 \, x^{2} e^{5} + 76 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-6*x*exp(5)+76,x, algorithm="giac")

[Out]

-3*x^2*e^5 + 76*x

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maple [A]  time = 0.02, size = 11, normalized size = 0.85

method	result	size
gosper	\(-x \left (3 x \,{\mathrm e}^{5}-76\right )\)	\(11\)
default	\(-3 x^{2} {\mathrm e}^{5}+76 x\)	\(12\)
norman	\(-3 x^{2} {\mathrm e}^{5}+76 x\)	\(12\)
risch	\(-3 x^{2} {\mathrm e}^{5}+76 x\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-6*x*exp(5)+76,x,method=_RETURNVERBOSE)

[Out]

-x*(3*x*exp(5)-76)

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maxima [A]  time = 0.52, size = 11, normalized size = 0.85 \begin {gather*} -3 \, x^{2} e^{5} + 76 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-6*x*exp(5)+76,x, algorithm="maxima")

[Out]

-3*x^2*e^5 + 76*x

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mupad [B]  time = 0.03, size = 10, normalized size = 0.77 \begin {gather*} -x\,\left (3\,x\,{\mathrm {e}}^5-76\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(76 - 6*x*exp(5),x)

[Out]

-x*(3*x*exp(5) - 76)

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sympy [A]  time = 0.05, size = 10, normalized size = 0.77 \begin {gather*} - 3 x^{2} e^{5} + 76 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-6*x*exp(5)+76,x)

[Out]

-3*x**2*exp(5) + 76*x

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