3.73.64 $\int \frac{900e^{\frac{450}{-1+2x}}}{1-4x+4x^2}dx$

Optimal. Leaf size=15 $$2-e^{\frac{450}{-1+2x}}$$

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Rubi [A]  time = 0.02, antiderivative size = 13, normalized size of antiderivative = 0.87, number of steps used = 3, number of rules used = 3, integrand size = 25, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.120, Rules used = {12, 27, 2209} $$\begin{array}{c}-e^{-\frac{450}{1-2x}}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(900*E^(450/(-1 + 2*x)))/(1 - 4*x + 4*x^2),x]

[Out]

-E^(-450/(1 - 2*x))

Rule 12

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

Rule 27

Int[(u_.)*((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[u*Cancel[(b/2 + c*x)^(2*p)/c^p], x] /; Fr
eeQ[{a, b, c}, x] && EqQ[b^2 - 4*a*c, 0] && IntegerQ[p]

Rule 2209

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[((e + f*x)^n*
F^(a + b*(c + d*x)^n))/(b*f*n*(c + d*x)^n*Log[F]), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =900\int \frac{e^{\frac{450}{-1+2x}}}{1-4x+4x^2}dx\\ & =900\int \frac{e^{\frac{450}{-1+2x}}}{(-1+2x{)}^2}dx\\ & =-e^{-\frac{450}{1-2x}}\end{array}\end{array}$$

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Mathematica [A]  time = 0.01, size = 13, normalized size = 0.87 $$\begin{array}{c}-e^{\frac{450}{-1+2x}}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(900*E^(450/(-1 + 2*x)))/(1 - 4*x + 4*x^2),x]

[Out]

-E^(450/(-1 + 2*x))

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fricas [A]  time = 0.72, size = 12, normalized size = 0.80 $$\begin{array}{c}-e^{\left(\frac{450}{2x-1}\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(900*exp(450/(2*x-1))/(4*x^2-4*x+1),x, algorithm="fricas")

[Out]

-e^(450/(2*x - 1))

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giac [A]  time = 0.20, size = 12, normalized size = 0.80 $$\begin{array}{c}-e^{\left(\frac{450}{2x-1}\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(900*exp(450/(2*x-1))/(4*x^2-4*x+1),x, algorithm="giac")

[Out]

-e^(450/(2*x - 1))

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maple [A]  time = 0.16, size = 13, normalized size = 0.87

method	result	size
gosper	$-{\mathrm{e}}^{\frac{450}{2x-1}}$	$13$
derivativedivides	$-{\mathrm{e}}^{\frac{450}{2x-1}}$	$13$
default	$-{\mathrm{e}}^{\frac{450}{2x-1}}$	$13$
risch	$-{\mathrm{e}}^{\frac{450}{2x-1}}$	$13$
norman	$\frac{-2x{\mathrm{e}}^{\frac{450}{2x-1}}+{\mathrm{e}}^{\frac{450}{2x-1}}}{2x-1}$	$33$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(900*exp(450/(2*x-1))/(4*x^2-4*x+1),x,method=_RETURNVERBOSE)

[Out]

-exp(450/(2*x-1))

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maxima [A]  time = 0.35, size = 12, normalized size = 0.80 $$\begin{array}{c}-e^{\left(\frac{450}{2x-1}\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(900*exp(450/(2*x-1))/(4*x^2-4*x+1),x, algorithm="maxima")

[Out]

-e^(450/(2*x - 1))

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mupad [B]  time = 0.11, size = 12, normalized size = 0.80 $$\begin{array}{c}-{\mathrm{e}}^{\frac{450}{2x-1}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((900*exp(450/(2*x - 1)))/(4*x^2 - 4*x + 1),x)

[Out]

-exp(450/(2*x - 1))

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sympy [A]  time = 0.18, size = 8, normalized size = 0.53 $$\begin{array}{c}-e^{\frac{450}{2x-1}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(900*exp(450/(2*x-1))/(4*x**2-4*x+1),x)

[Out]

-exp(450/(2*x - 1))

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