3.72.93 \(\int (-240-8 e^{\frac {6}{5+e^3}}+32 x) \, dx\)

Optimal. Leaf size=20 \[ \left (-30-e^{\frac {6}{5+e^3}}+4 x\right )^2 \]

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Rubi [A]  time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.10, number of steps used = 1, number of rules used = 0, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 16 x^2-8 \left (30+e^{\frac {6}{5+e^3}}\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-240 - 8*E^(6/(5 + E^3)) + 32*x,x]

[Out]

-8*(30 + E^(6/(5 + E^3)))*x + 16*x^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-8 \left (30+e^{\frac {6}{5+e^3}}\right ) x+16 x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 23, normalized size = 1.15 \begin {gather*} -240 x-8 e^{\frac {6}{5+e^3}} x+16 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-240 - 8*E^(6/(5 + E^3)) + 32*x,x]

[Out]

-240*x - 8*E^(6/(5 + E^3))*x + 16*x^2

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fricas [A]  time = 1.23, size = 21, normalized size = 1.05 \begin {gather*} 16 \, x^{2} - 8 \, x e^{\left (\frac {6}{e^{3} + 5}\right )} - 240 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*exp(3/(exp(3)+5))^2+32*x-240,x, algorithm="fricas")

[Out]

16*x^2 - 8*x*e^(6/(e^3 + 5)) - 240*x

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giac [A]  time = 0.19, size = 21, normalized size = 1.05 \begin {gather*} 16 \, x^{2} - 8 \, x e^{\left (\frac {6}{e^{3} + 5}\right )} - 240 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*exp(3/(exp(3)+5))^2+32*x-240,x, algorithm="giac")

[Out]

16*x^2 - 8*x*e^(6/(e^3 + 5)) - 240*x

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maple [A]  time = 0.02, size = 20, normalized size = 1.00

method	result	size
gosper	\(-8 x \left ({\mathrm e}^{\frac {6}{{\mathrm e}^{3}+5}}-2 x +30\right )\)	\(20\)
norman	\(\left (-8 \,{\mathrm e}^{\frac {6}{{\mathrm e}^{3}+5}}-240\right ) x +16 x^{2}\)	\(22\)
risch	\(-8 \,{\mathrm e}^{\frac {6}{{\mathrm e}^{3}+5}} x +16 x^{2}-240 x\)	\(22\)
default	\(-8 \,{\mathrm e}^{\frac {6}{{\mathrm e}^{3}+5}} x +16 x^{2}-240 x\)	\(24\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-8*exp(3/(exp(3)+5))^2+32*x-240,x,method=_RETURNVERBOSE)

[Out]

-8*x*(exp(3/(exp(3)+5))^2-2*x+30)

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maxima [A]  time = 0.36, size = 21, normalized size = 1.05 \begin {gather*} 16 \, x^{2} - 8 \, x e^{\left (\frac {6}{e^{3} + 5}\right )} - 240 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*exp(3/(exp(3)+5))^2+32*x-240,x, algorithm="maxima")

[Out]

16*x^2 - 8*x*e^(6/(e^3 + 5)) - 240*x

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mupad [B]  time = 0.05, size = 22, normalized size = 1.10 \begin {gather*} 16\,x^2-x\,\left (8\,{\mathrm {e}}^{\frac {6}{{\mathrm {e}}^3+5}}+240\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(32*x - 8*exp(6/(exp(3) + 5)) - 240,x)

[Out]

16*x^2 - x*(8*exp(6/(exp(3) + 5)) + 240)

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sympy [A]  time = 0.07, size = 19, normalized size = 0.95 \begin {gather*} 16 x^{2} + x \left (-240 - 8 e^{\frac {6}{5 + e^{3}}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*exp(3/(exp(3)+5))**2+32*x-240,x)

[Out]

16*x**2 + x*(-240 - 8*exp(6/(5 + exp(3))))

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