3.41.29 \(\int (10+2 e^6+2 x) \, dx\)

Optimal. Leaf size=8 \[ \left (5+e^6+x\right )^2 \]

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Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.50, number of steps used = 1, number of rules used = 0, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x^2+2 \left (5+e^6\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[10 + 2*E^6 + 2*x,x]

[Out]

2*(5 + E^6)*x + x^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=2 \left (5+e^6\right ) x+x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 1.62 \begin {gather*} 10 x+2 e^6 x+x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[10 + 2*E^6 + 2*x,x]

[Out]

10*x + 2*E^6*x + x^2

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fricas [A]  time = 0.97, size = 12, normalized size = 1.50 \begin {gather*} x^{2} + 2 \, x e^{6} + 10 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(6)+2*x+10,x, algorithm="fricas")

[Out]

x^2 + 2*x*e^6 + 10*x

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giac [A]  time = 0.18, size = 12, normalized size = 1.50 \begin {gather*} x^{2} + 2 \, x e^{6} + 10 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(6)+2*x+10,x, algorithm="giac")

[Out]

x^2 + 2*x*e^6 + 10*x

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maple [A]  time = 0.02, size = 10, normalized size = 1.25

method	result	size
gosper	\(x \left (x +2 \,{\mathrm e}^{6}+10\right )\)	\(10\)
default	\(2 x \,{\mathrm e}^{6}+x^{2}+10 x\)	\(13\)
norman	\(x^{2}+\left (2 \,{\mathrm e}^{6}+10\right ) x\)	\(13\)
risch	\(2 x \,{\mathrm e}^{6}+x^{2}+10 x\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*exp(6)+2*x+10,x,method=_RETURNVERBOSE)

[Out]

x*(x+2*exp(6)+10)

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maxima [A]  time = 0.35, size = 12, normalized size = 1.50 \begin {gather*} x^{2} + 2 \, x e^{6} + 10 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(6)+2*x+10,x, algorithm="maxima")

[Out]

x^2 + 2*x*e^6 + 10*x

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mupad [B]  time = 2.96, size = 9, normalized size = 1.12 \begin {gather*} x\,\left (x+2\,{\mathrm {e}}^6+10\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + 2*exp(6) + 10,x)

[Out]

x*(x + 2*exp(6) + 10)

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sympy [A]  time = 0.05, size = 10, normalized size = 1.25 \begin {gather*} x^{2} + x \left (10 + 2 e^{6}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(6)+2*x+10,x)

[Out]

x**2 + x*(10 + 2*exp(6))

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