3.41.85 \(\int (2+3 e^5 x^2) \, dx\)

Optimal. Leaf size=12 \[ -5+2 x+e^5 x^3 \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.92, 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*} e^5 x^3+2 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2 + 3*E^5*x^2,x]

[Out]

2*x + E^5*x^3

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.92 \begin {gather*} 2 x+e^5 x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2 + 3*E^5*x^2,x]

[Out]

2*x + E^5*x^3

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fricas [A]  time = 0.77, size = 10, normalized size = 0.83 \begin {gather*} x^{3} e^{5} + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x^2*exp(5)+2,x, algorithm="fricas")

[Out]

x^3*e^5 + 2*x

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giac [A]  time = 0.13, size = 10, normalized size = 0.83 \begin {gather*} x^{3} e^{5} + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x^2*exp(5)+2,x, algorithm="giac")

[Out]

x^3*e^5 + 2*x

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

method	result	size
gosper	\(x^{3} {\mathrm e}^{5}+2 x\)	\(11\)
default	\(x^{3} {\mathrm e}^{5}+2 x\)	\(11\)
norman	\(x^{3} {\mathrm e}^{5}+2 x\)	\(11\)
risch	\(x^{3} {\mathrm e}^{5}+2 x\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*x^2*exp(5)+2,x,method=_RETURNVERBOSE)

[Out]

x^3*exp(5)+2*x

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maxima [A]  time = 0.36, size = 10, normalized size = 0.83 \begin {gather*} x^{3} e^{5} + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x^2*exp(5)+2,x, algorithm="maxima")

[Out]

x^3*e^5 + 2*x

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mupad [B]  time = 0.02, size = 10, normalized size = 0.83 \begin {gather*} {\mathrm {e}}^5\,x^3+2\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*x^2*exp(5) + 2,x)

[Out]

2*x + x^3*exp(5)

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sympy [A]  time = 0.05, size = 8, normalized size = 0.67 \begin {gather*} x^{3} e^{5} + 2 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x**2*exp(5)+2,x)

[Out]

x**3*exp(5) + 2*x

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