3.89.80 $\int (e^{4}x\log (4)+2e^{4}x\log (4)\log (x))dx$

Optimal. Leaf size=15 $$\frac{9}{5}+e^4{x}^2\log (4)\log (x)$$

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Rubi [A]  time = 0.01, antiderivative size = 11, normalized size of antiderivative = 0.73, number of steps used = 2, number of rules used = 1, integrand size = 18, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.056, Rules used = {2304} $$\begin{array}{c}{e}^4{x}^2\log (4)\log (x)\end{array}$$

Antiderivative was successfully verified.

[In]

Int[E^4*x*Log[4] + 2*E^4*x*Log[4]*Log[x],x]

[Out]

E^4*x^2*Log[4]*Log[x]

Rule 2304

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Log[c*x^
n]))/(d*(m + 1)), x] - Simp[(b*n*(d*x)^(m + 1))/(d*(m + 1)^2), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1
]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\frac{1}{2}{e}^4{x}^2\log (4)+(2e^4\log (4))\int x\log (x)dx\\ & =e^4{x}^2\log (4)\log (x)\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.73 $$\begin{array}{c}{e}^4{x}^2\log (4)\log (x)\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[E^4*x*Log[4] + 2*E^4*x*Log[4]*Log[x],x]

[Out]

E^4*x^2*Log[4]*Log[x]

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fricas [A]  time = 0.55, size = 11, normalized size = 0.73 $$\begin{array}{c}2x^2{e}^4\log (2)\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x*exp(1)^4*log(2)*log(x)+2*x*exp(1)^4*log(2),x, algorithm="fricas")

[Out]

2*x^2*e^4*log(2)*log(x)

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giac [B]  time = 1.16, size = 27, normalized size = 1.80 $$\begin{array}{c}{x}^2{e}^4\log (2)+(2x^2\log (x)-x^2)e^4\log (2)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x*exp(1)^4*log(2)*log(x)+2*x*exp(1)^4*log(2),x, algorithm="giac")

[Out]

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

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maple [A]  time = 0.03, size = 12, normalized size = 0.80

method	result	size
risch	$2\ln (x)\ln (2){\mathrm{e}}^4{x}^2$	$12$
default	$2\ln (x)\ln (2){\mathrm{e}}^4{x}^2$	$14$
norman	$2\ln (x)\ln (2){\mathrm{e}}^4{x}^2$	$14$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*x*exp(1)^4*ln(2)*ln(x)+2*x*exp(1)^4*ln(2),x,method=_RETURNVERBOSE)

[Out]

2*ln(x)*ln(2)*exp(4)*x^2

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maxima [B]  time = 0.37, size = 27, normalized size = 1.80 $$\begin{array}{c}{x}^2{e}^4\log (2)+(2x^2\log (x)-x^2)e^4\log (2)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x*exp(1)^4*log(2)*log(x)+2*x*exp(1)^4*log(2),x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 5.12, size = 11, normalized size = 0.73 $$\begin{array}{c}2x^2{\mathrm{e}}^4\ln (2)\ln (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x*exp(4)*log(2) + 4*x*exp(4)*log(2)*log(x),x)

[Out]

2*x^2*exp(4)*log(2)*log(x)

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sympy [A]  time = 0.10, size = 14, normalized size = 0.93 $$\begin{array}{c}2x^2{e}^4\log (2)\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x*exp(1)**4*ln(2)*ln(x)+2*x*exp(1)**4*ln(2),x)

[Out]

2*x**2*exp(4)*log(2)*log(x)

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