3.86.8 \(\int (-3+e^{20+24 x-4 x^5} (72-60 x^4)) \, dx\)

Optimal. Leaf size=23 \[ 3 \left (e^{20-8 x+4 x \left (8-x^4\right )}-x\right ) \]

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Rubi [A]  time = 0.04, antiderivative size = 18, normalized size of antiderivative = 0.78, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {6706} \begin {gather*} 3 e^{-4 x^5+24 x+20}-3 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-3 + E^(20 + 24*x - 4*x^5)*(72 - 60*x^4),x]

[Out]

3*E^(20 + 24*x - 4*x^5) - 3*x

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} &=-3 x+\int e^{20+24 x-4 x^5} \left (72-60 x^4\right ) \, dx\\ &=3 e^{20+24 x-4 x^5}-3 x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.06, size = 18, normalized size = 0.78 \begin {gather*} 3 e^{20+24 x-4 x^5}-3 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-3 + E^(20 + 24*x - 4*x^5)*(72 - 60*x^4),x]

[Out]

3*E^(20 + 24*x - 4*x^5) - 3*x

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fricas [A]  time = 0.60, size = 17, normalized size = 0.74 \begin {gather*} -3 \, x + 3 \, e^{\left (-4 \, x^{5} + 24 \, x + 20\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-60*x^4+72)*exp(-x^5+6*x+5)^4-3,x, algorithm="fricas")

[Out]

-3*x + 3*e^(-4*x^5 + 24*x + 20)

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giac [A]  time = 0.12, size = 17, normalized size = 0.74 \begin {gather*} -3 \, x + 3 \, e^{\left (-4 \, x^{5} + 24 \, x + 20\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-60*x^4+72)*exp(-x^5+6*x+5)^4-3,x, algorithm="giac")

[Out]

-3*x + 3*e^(-4*x^5 + 24*x + 20)

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maple [A]  time = 0.02, size = 20, normalized size = 0.87

method	result	size
default	\(-3 x +3 \,{\mathrm e}^{-4 x^{5}+24 x +20}\)	\(20\)
norman	\(-3 x +3 \,{\mathrm e}^{-4 x^{5}+24 x +20}\)	\(20\)
risch	\(-3 x +3 \,{\mathrm e}^{-4 \left (x +1\right ) \left (x^{4}-x^{3}+x^{2}-x -5\right )}\)	\(29\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-60*x^4+72)*exp(-x^5+6*x+5)^4-3,x,method=_RETURNVERBOSE)

[Out]

-3*x+3*exp(-x^5+6*x+5)^4

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maxima [A]  time = 0.37, size = 17, normalized size = 0.74 \begin {gather*} -3 \, x + 3 \, e^{\left (-4 \, x^{5} + 24 \, x + 20\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-60*x^4+72)*exp(-x^5+6*x+5)^4-3,x, algorithm="maxima")

[Out]

-3*x + 3*e^(-4*x^5 + 24*x + 20)

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mupad [B]  time = 5.29, size = 18, normalized size = 0.78 \begin {gather*} 3\,{\mathrm {e}}^{24\,x}\,{\mathrm {e}}^{20}\,{\mathrm {e}}^{-4\,x^5}-3\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- exp(24*x - 4*x^5 + 20)*(60*x^4 - 72) - 3,x)

[Out]

3*exp(24*x)*exp(20)*exp(-4*x^5) - 3*x

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sympy [A]  time = 0.10, size = 15, normalized size = 0.65 \begin {gather*} - 3 x + 3 e^{- 4 x^{5} + 24 x + 20} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-60*x**4+72)*exp(-x**5+6*x+5)**4-3,x)

[Out]

-3*x + 3*exp(-4*x**5 + 24*x + 20)

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