3.95.24 \(\int (15+\sqrt [25]{e}+2 x) \, dx\)

Optimal. Leaf size=12 \[ (2+x) \left (13+\sqrt [25]{e}+x\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.08, 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+\left (15+\sqrt [25]{e}\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[15 + E^(1/25) + 2*x,x]

[Out]

(15 + E^(1/25))*x + x^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\left (15+\sqrt [25]{e}\right ) x+x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 1.17 \begin {gather*} 15 x+\sqrt [25]{e} x+x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[15 + E^(1/25) + 2*x,x]

[Out]

15*x + E^(1/25)*x + x^2

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fricas [A]  time = 0.63, size = 11, normalized size = 0.92 \begin {gather*} x^{2} + x e^{\frac {1}{25}} + 15 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(1/25)+2*x+15,x, algorithm="fricas")

[Out]

x^2 + x*e^(1/25) + 15*x

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giac [A]  time = 0.16, size = 11, normalized size = 0.92 \begin {gather*} x^{2} + x e^{\frac {1}{25}} + 15 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(1/25)+2*x+15,x, algorithm="giac")

[Out]

x^2 + x*e^(1/25) + 15*x

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maple [A]  time = 0.02, size = 11, normalized size = 0.92

method	result	size
norman	\(x^{2}+\left ({\mathrm e}^{\frac {1}{25}}+15\right ) x\)	\(11\)
gosper	\(x \,{\mathrm e}^{\frac {1}{25}}+x^{2}+15 x\)	\(12\)
default	\(x \,{\mathrm e}^{\frac {1}{25}}+x^{2}+15 x\)	\(12\)
risch	\(x \,{\mathrm e}^{\frac {1}{25}}+x^{2}+15 x\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(1/25)+2*x+15,x,method=_RETURNVERBOSE)

[Out]

x^2+(exp(1/25)+15)*x

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maxima [A]  time = 0.35, size = 11, normalized size = 0.92 \begin {gather*} x^{2} + x e^{\frac {1}{25}} + 15 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(1/25)+2*x+15,x, algorithm="maxima")

[Out]

x^2 + x*e^(1/25) + 15*x

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mupad [B]  time = 5.36, size = 10, normalized size = 0.83 \begin {gather*} x^2+\left ({\mathrm {e}}^{1/25}+15\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + exp(1/25) + 15,x)

[Out]

x*(exp(1/25) + 15) + x^2

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sympy [A]  time = 0.05, size = 10, normalized size = 0.83 \begin {gather*} x^{2} + x \left (e^{\frac {1}{25}} + 15\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(1/25)+2*x+15,x)

[Out]

x**2 + x*(exp(1/25) + 15)

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