3.69.51 $\int e^{(4x+3x^2+4x^3)\log (2)-3x\log (2)\log (4)}((4+6x+12x^2)\log (2)-3\log (2)\log (4))dx$

Optimal. Leaf size=20 $$2^{x(4(1+x^2)-3(-x+\log (4)))}$$

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Rubi [A]  time = 0.09, antiderivative size = 26, normalized size of antiderivative = 1.30, number of steps used = 1, number of rules used = 1, integrand size = 48, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.021, Rules used = {6706} $$\begin{array}{c}{2}^{4x^3+3x^2+4x}{e}^{-3x\log (2)\log (4)}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[E^((4*x + 3*x^2 + 4*x^3)*Log[2] - 3*x*Log[2]*Log[4])*((4 + 6*x + 12*x^2)*Log[2] - 3*Log[2]*Log[4]),x]

[Out]

2^(4*x + 3*x^2 + 4*x^3)/E^(3*x*Log[2]*Log[4])

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =2^{4x+3x^2+4x^3}{e}^{-3x\log (2)\log (4)}\end{array}\end{array}$$

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Mathematica [F]  time = 0.48, size = 0, normalized size = 0.00 $$\begin{array}{c}\int e^{(4x+3x^2+4x^3)\log (2)-3x\log (2)\log (4)}((4+6x+12x^2)\log (2)-3\log (2)\log (4))dx\end{array}$$

Verification is not applicable to the result.

[In]

Integrate[E^((4*x + 3*x^2 + 4*x^3)*Log[2] - 3*x*Log[2]*Log[4])*((4 + 6*x + 12*x^2)*Log[2] - 3*Log[2]*Log[4]),x
]

[Out]

Integrate[E^((4*x + 3*x^2 + 4*x^3)*Log[2] - 3*x*Log[2]*Log[4])*((4 + 6*x + 12*x^2)*Log[2] - 3*Log[2]*Log[4]),
x]

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fricas [A]  time = 0.56, size = 26, normalized size = 1.30 $$\begin{array}{c}{e}^{(-6x\log (2{)}^2+(4x^3+3x^2+4x)\log (2))}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-6*log(2)^2+(12*x^2+6*x+4)*log(2))*exp(-6*x*log(2)^2+(4*x^3+3*x^2+4*x)*log(2)),x, algorithm="fricas
")

[Out]

e^(-6*x*log(2)^2 + (4*x^3 + 3*x^2 + 4*x)*log(2))

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giac [A]  time = 0.25, size = 28, normalized size = 1.40 $$\begin{array}{c}{e}^{(4x^3\log (2)+3x^2\log (2)-6x\log (2{)}^2+4x\log (2))}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-6*log(2)^2+(12*x^2+6*x+4)*log(2))*exp(-6*x*log(2)^2+(4*x^3+3*x^2+4*x)*log(2)),x, algorithm="giac")

[Out]

e^(4*x^3*log(2) + 3*x^2*log(2) - 6*x*log(2)^2 + 4*x*log(2))

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maple [A]  time = 0.04, size = 24, normalized size = 1.20

method	result	size
risch	$2^{x(4x^2+3x+4)}{\mathrm{e}}^{-6x\ln (2{)}^2}$	$24$
derivativedivides	${\mathrm{e}}^{-6x\ln (2{)}^2+(4x^3+3x^2+4x)\ln (2)}$	$27$
default	${\mathrm{e}}^{-6x\ln (2{)}^2+(4x^3+3x^2+4x)\ln (2)}$	$27$
norman	${\mathrm{e}}^{-6x\ln (2{)}^2+(4x^3+3x^2+4x)\ln (2)}$	$27$
gosper	${\mathrm{e}}^{4x^3\ln (2)-6x\ln (2{)}^2+3x^2\ln (2)+4x\ln (2)}$	$29$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-6*ln(2)^2+(12*x^2+6*x+4)*ln(2))*exp(-6*x*ln(2)^2+(4*x^3+3*x^2+4*x)*ln(2)),x,method=_RETURNVERBOSE)

[Out]

2^(x*(4*x^2+3*x+4))*exp(-6*x*ln(2)^2)

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maxima [A]  time = 0.53, size = 28, normalized size = 1.40 $$\begin{array}{c}{e}^{(4x^3\log (2)+3x^2\log (2)-6x\log (2{)}^2+4x\log (2))}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-6*log(2)^2+(12*x^2+6*x+4)*log(2))*exp(-6*x*log(2)^2+(4*x^3+3*x^2+4*x)*log(2)),x, algorithm="maxima
")

[Out]

e^(4*x^3*log(2) + 3*x^2*log(2) - 6*x*log(2)^2 + 4*x*log(2))

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mupad [B]  time = 4.28, size = 28, normalized size = 1.40 $$\begin{array}{c}{2}^{4x}{2}^{3x^2}{2}^{4x^3}{\mathrm{e}}^{-6x{\ln (2)}^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(log(2)*(4*x + 3*x^2 + 4*x^3) - 6*x*log(2)^2)*(log(2)*(6*x + 12*x^2 + 4) - 6*log(2)^2),x)

[Out]

2^(4*x)*2^(3*x^2)*2^(4*x^3)*exp(-6*x*log(2)^2)

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sympy [A]  time = 0.15, size = 26, normalized size = 1.30 $$\begin{array}{c}{e}^{-6x\log {(2)}^2+(4x^3+3x^2+4x)\log (2)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-6*ln(2)**2+(12*x**2+6*x+4)*ln(2))*exp(-6*x*ln(2)**2+(4*x**3+3*x**2+4*x)*ln(2)),x)

[Out]

exp(-6*x*log(2)**2 + (4*x**3 + 3*x**2 + 4*x)*log(2))

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