3.3.73 \(\int e^{2+2 x+x^5} (2+5 x^4) \, dx\)

Optimal. Leaf size=14 \[ e^{2-x+x \left (3+x^4\right )} \]

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Rubi [A]  time = 0.06, antiderivative size = 10, normalized size of antiderivative = 0.71, number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {6706} \begin {gather*} e^{x^5+2 x+2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(2 + 2*x + x^5)*(2 + 5*x^4),x]

[Out]

E^(2 + 2*x + x^5)

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

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

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Mathematica [A]  time = 0.03, size = 10, normalized size = 0.71 \begin {gather*} e^{2+2 x+x^5} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(2 + 2*x + x^5)*(2 + 5*x^4),x]

[Out]

E^(2 + 2*x + x^5)

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fricas [A]  time = 0.60, size = 9, normalized size = 0.64 \begin {gather*} e^{\left (x^{5} + 2 \, x + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5*x^4+2)*exp(x^5+2*x+2),x, algorithm="fricas")

[Out]

e^(x^5 + 2*x + 2)

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giac [A]  time = 0.71, size = 9, normalized size = 0.64 \begin {gather*} e^{\left (x^{5} + 2 \, x + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5*x^4+2)*exp(x^5+2*x+2),x, algorithm="giac")

[Out]

e^(x^5 + 2*x + 2)

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maple [A]  time = 0.03, size = 10, normalized size = 0.71

method	result	size
gosper	\({\mathrm e}^{x^{5}+2 x +2}\)	\(10\)
derivativedivides	\({\mathrm e}^{x^{5}+2 x +2}\)	\(10\)
default	\({\mathrm e}^{x^{5}+2 x +2}\)	\(10\)
norman	\({\mathrm e}^{x^{5}+2 x +2}\)	\(10\)
risch	\({\mathrm e}^{x^{5}+2 x +2}\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((5*x^4+2)*exp(x^5+2*x+2),x,method=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.55, size = 9, normalized size = 0.64 \begin {gather*} e^{\left (x^{5} + 2 \, x + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5*x^4+2)*exp(x^5+2*x+2),x, algorithm="maxima")

[Out]

e^(x^5 + 2*x + 2)

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mupad [B]  time = 0.04, size = 11, normalized size = 0.79 \begin {gather*} {\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{x^5}\,{\mathrm {e}}^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(2*x + x^5 + 2)*(5*x^4 + 2),x)

[Out]

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

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sympy [A]  time = 0.08, size = 8, normalized size = 0.57 \begin {gather*} e^{x^{5} + 2 x + 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5*x**4+2)*exp(x**5+2*x+2),x)

[Out]

exp(x**5 + 2*x + 2)

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