3.42.49 \(\int (-e^{3+e^5+x}+x^3) \, dx\)

Optimal. Leaf size=18 \[ -e^{3+e^5+x}+\frac {x^4}{4} \]

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Rubi [A]  time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2194} \begin {gather*} \frac {x^4}{4}-e^{x+e^5+3} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-E^(3 + E^5 + x) + x^3,x]

[Out]

-E^(3 + E^5 + x) + x^4/4

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {x^4}{4}-\int e^{3+e^5+x} \, dx\\ &=-e^{3+e^5+x}+\frac {x^4}{4}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 18, normalized size = 1.00 \begin {gather*} -e^{3+e^5+x}+\frac {x^4}{4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-E^(3 + E^5 + x) + x^3,x]

[Out]

-E^(3 + E^5 + x) + x^4/4

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fricas [A]  time = 0.54, size = 14, normalized size = 0.78 \begin {gather*} \frac {1}{4} \, x^{4} - e^{\left (x + e^{5} + 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/4*x^4 - e^(x + e^5 + 3)

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giac [A]  time = 0.13, size = 14, normalized size = 0.78 \begin {gather*} \frac {1}{4} \, x^{4} - e^{\left (x + e^{5} + 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/4*x^4 - e^(x + e^5 + 3)

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maple [A]  time = 0.02, size = 15, normalized size = 0.83

method	result	size
derivativedivides	\(\frac {x^{4}}{4}-{\mathrm e}^{{\mathrm e}^{5}+3+x}\)	\(15\)
default	\(\frac {x^{4}}{4}-{\mathrm e}^{{\mathrm e}^{5}+3+x}\)	\(15\)
norman	\(\frac {x^{4}}{4}-{\mathrm e}^{{\mathrm e}^{5}+3+x}\)	\(15\)
risch	\(\frac {x^{4}}{4}-{\mathrm e}^{{\mathrm e}^{5}+3+x}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/4*x^4-exp(exp(5)+3+x)

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maxima [A]  time = 0.36, size = 14, normalized size = 0.78 \begin {gather*} \frac {1}{4} \, x^{4} - e^{\left (x + e^{5} + 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/4*x^4 - e^(x + e^5 + 3)

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mupad [B]  time = 0.06, size = 15, normalized size = 0.83 \begin {gather*} \frac {x^4}{4}-{\mathrm {e}}^3\,{\mathrm {e}}^{{\mathrm {e}}^5}\,{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^3 - exp(x + exp(5) + 3),x)

[Out]

x^4/4 - exp(3)*exp(exp(5))*exp(x)

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sympy [A]  time = 0.08, size = 12, normalized size = 0.67 \begin {gather*} \frac {x^{4}}{4} - e^{x + 3 + e^{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x**4/4 - exp(x + 3 + exp(5))

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