3.100.94 \(\int (-20-e-10 x) \, dx\)

Optimal. Leaf size=11 \[ (-4-x) (e+5 x) \]

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Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.09, 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*} -5 x^2-(20+e) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-20 - E - 10*x,x]

[Out]

-((20 + E)*x) - 5*x^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-((20+e) x)-5 x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 1.18 \begin {gather*} -20 x-e x-5 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-20 - E - 10*x,x]

[Out]

-20*x - E*x - 5*x^2

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fricas [A]  time = 1.16, size = 14, normalized size = 1.27 \begin {gather*} -5 \, x^{2} - x e - 20 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(1)-10*x-20,x, algorithm="fricas")

[Out]

-5*x^2 - x*e - 20*x

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giac [A]  time = 0.20, size = 14, normalized size = 1.27 \begin {gather*} -5 \, x^{2} - x e - 20 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(1)-10*x-20,x, algorithm="giac")

[Out]

-5*x^2 - x*e - 20*x

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maple [A]  time = 0.02, size = 11, normalized size = 1.00

method	result	size
gosper	\(-x \left (5 x +{\mathrm e}+20\right )\)	\(11\)
default	\(-x \,{\mathrm e}-5 x^{2}-20 x\)	\(15\)
norman	\(\left (-{\mathrm e}-20\right ) x -5 x^{2}\)	\(15\)
risch	\(-x \,{\mathrm e}-5 x^{2}-20 x\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(1)-10*x-20,x,method=_RETURNVERBOSE)

[Out]

-x*(5*x+exp(1)+20)

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maxima [A]  time = 0.36, size = 14, normalized size = 1.27 \begin {gather*} -5 \, x^{2} - x e - 20 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(1)-10*x-20,x, algorithm="maxima")

[Out]

-5*x^2 - x*e - 20*x

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mupad [B]  time = 0.08, size = 13, normalized size = 1.18 \begin {gather*} -5\,x^2+\left (-\mathrm {e}-20\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- 10*x - exp(1) - 20,x)

[Out]

- x*(exp(1) + 20) - 5*x^2

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sympy [A]  time = 0.05, size = 12, normalized size = 1.09 \begin {gather*} - 5 x^{2} + x \left (-20 - e\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(1)-10*x-20,x)

[Out]

-5*x**2 + x*(-20 - E)

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