3.69.75 $\int \frac{152^{1-2e^{e^2}}{e}^{e^2}(6-2e^6-3x{)}^{2e^{e^2}}}{-6+2e^6+3x}dx$

Optimal. Leaf size=22 $$5{(3-e^6-\frac{3x}{2})}^{2e^{e^2}}$$

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Rubi [A]  time = 0.01, antiderivative size = 32, normalized size of antiderivative = 1.45, number of steps used = 3, number of rules used = 3, integrand size = 48, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.062, Rules used = {12, 21, 32} $$\begin{array}{c}54^{-e^{e^2}}{(2(3-e^6)-3x)}^{2e^{e^2}}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(15*2^(1 - 2*E^E^2)*E^E^2*(6 - 2*E^6 - 3*x)^(2*E^E^2))/(-6 + 2*E^6 + 3*x),x]

[Out]

(5*(2*(3 - E^6) - 3*x)^(2*E^E^2))/4^E^E^2

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 21

Int[(u_.)*((a_) + (b_.)*(v_))^(m_.)*((c_) + (d_.)*(v_))^(n_.), x_Symbol] :> Dist[(b/d)^m, Int[u*(c + d*v)^(m +
n), x], x] /; FreeQ[{a, b, c, d, n}, x] && EqQ[b*c - a*d, 0] && IntegerQ[m] && ( !IntegerQ[n] || SimplerQ[c +
d*x, a + b*x])

Rule 32

Int[((a_.) + (b_.)*(x_))^(m_), x_Symbol] :> Simp[(a + b*x)^(m + 1)/(b*(m + 1)), x] /; FreeQ[{a, b, m}, x] && N
eQ[m, -1]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\left(152^{1-2e^{e^2}}{e}^{e^2}\right)\int \frac{{(6-2e^6-3x)}^{2e^{e^2}}}{-6+2e^6+3x}dx\\ & =-(\left(152^{1-2e^{e^2}}{e}^{e^2}\right)\int {(6-2e^6-3x)}^{-1+2e^{e^2}}dx)\\ & =54^{-e^{e^2}}{(2(3-e^6)-3x)}^{2e^{e^2}}\end{array}\end{array}$$

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Mathematica [A]  time = 0.02, size = 22, normalized size = 1.00 $$\begin{array}{c}5{(3-e^6-\frac{3x}{2})}^{2e^{e^2}}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(15*2^(1 - 2*E^E^2)*E^E^2*(6 - 2*E^6 - 3*x)^(2*E^E^2))/(-6 + 2*E^6 + 3*x),x]

[Out]

5*(3 - E^6 - (3*x)/2)^(2*E^E^2)

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fricas [A]  time = 2.78, size = 17, normalized size = 0.77 $$\begin{array}{c}5{(-\frac{3}{2}x-e^6+3)}^{2e^{\left(e^2\right)}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(30*exp(exp(2))*exp(exp(exp(2))*log(-exp(6)-3/2*x+3))^2/(2*exp(6)+3*x-6),x, algorithm="fricas")

[Out]

5*(-3/2*x - e^6 + 3)^(2*e^(e^2))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 $$\begin{array}{c}\int \frac{30{(-\frac{3}{2}x-e^6+3)}^{2e^{\left(e^2\right)}}{e}^{\left(e^2\right)}}{3x+2e^6-6}dx\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(30*exp(exp(2))*exp(exp(exp(2))*log(-exp(6)-3/2*x+3))^2/(2*exp(6)+3*x-6),x, algorithm="giac")

[Out]

integrate(30*(-3/2*x - e^6 + 3)^(2*e^(e^2))*e^(e^2)/(3*x + 2*e^6 - 6), x)

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maple [A]  time = 0.09, size = 18, normalized size = 0.82

method	result	size
risch	$5{(-{\mathrm{e}}^6-\frac{3x}{2}+3)}^{2{\mathrm{e}}^{{\mathrm{e}}^2}}$	$18$
gosper	$5{\mathrm{e}}^{2{\mathrm{e}}^{{\mathrm{e}}^2}\ln (-{\mathrm{e}}^6-\frac{3x}{2}+3)}$	$20$
norman	$5{\mathrm{e}}^{2{\mathrm{e}}^{{\mathrm{e}}^2}\ln (-{\mathrm{e}}^6-\frac{3x}{2}+3)}$	$20$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(30*exp(exp(2))*exp(exp(exp(2))*ln(-exp(6)-3/2*x+3))^2/(2*exp(6)+3*x-6),x,method=_RETURNVERBOSE)

[Out]

5*((-exp(6)-3/2*x+3)^exp(exp(2)))^2

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maxima [A]  time = 0.46, size = 26, normalized size = 1.18 $$\begin{array}{c}\frac{5{(-3x-2e^6+6)}^{2e^{\left(e^2\right)}}}{2^{2e^{\left(e^2\right)}}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(30*exp(exp(2))*exp(exp(exp(2))*log(-exp(6)-3/2*x+3))^2/(2*exp(6)+3*x-6),x, algorithm="maxima")

[Out]

5*(-3*x - 2*e^6 + 6)^(2*e^(e^2))/2^(2*e^(e^2))

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mupad [B]  time = 0.32, size = 17, normalized size = 0.77 $$\begin{array}{c}5{(3-{\mathrm{e}}^6-\frac{3x}{2})}^{2{\mathrm{e}}^{{\mathrm{e}}^2}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((30*exp(exp(2))*(3 - exp(6) - (3*x)/2)^(2*exp(exp(2))))/(3*x + 2*exp(6) - 6),x)

[Out]

5*(3 - exp(6) - (3*x)/2)^(2*exp(exp(2)))

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sympy [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 $$\begin{array}{c}\text{Exception raised: TypeError}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(30*exp(exp(2))*exp(exp(exp(2))*ln(-exp(6)-3/2*x+3))**2/(2*exp(6)+3*x-6),x)

[Out]

Exception raised: TypeError

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