3.1621 \(\int \frac{3+5 x}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=18 \[ \frac{(5 x+3)^2}{22 (1-2 x)^2} \]

[Out]

(3 + 5*x)^2/(22*(1 - 2*x)^2)

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Rubi [A]  time = 0.0110893, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{(5 x+3)^2}{22 (1-2 x)^2} \]

Antiderivative was successfully verified.

[In]  Int[(3 + 5*x)/(1 - 2*x)^3,x]

[Out]

(3 + 5*x)^2/(22*(1 - 2*x)^2)

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Rubi in Sympy [A]  time = 2.48369, size = 14, normalized size = 0.78 \[ \frac{\left (5 x + 3\right )^{2}}{22 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((3+5*x)/(1-2*x)**3,x)

[Out]

(5*x + 3)**2/(22*(-2*x + 1)**2)

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Mathematica [A]  time = 0.00599392, size = 16, normalized size = 0.89 \[ \frac{20 x+1}{8 (1-2 x)^2} \]

Antiderivative was successfully verified.

[In]  Integrate[(3 + 5*x)/(1 - 2*x)^3,x]

[Out]

(1 + 20*x)/(8*(1 - 2*x)^2)

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Maple [A]  time = 0.007, size = 20, normalized size = 1.1 \[{\frac{11}{8\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{5}{-4+8\,x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+5*x)/(1-2*x)^3,x)

[Out]

11/8/(-1+2*x)^2+5/4/(-1+2*x)

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Maxima [A]  time = 1.33175, size = 26, normalized size = 1.44 \[ \frac{20 \, x + 1}{8 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)/(2*x - 1)^3,x, algorithm="maxima")

[Out]

1/8*(20*x + 1)/(4*x^2 - 4*x + 1)

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Fricas [A]  time = 0.205862, size = 26, normalized size = 1.44 \[ \frac{20 \, x + 1}{8 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)/(2*x - 1)^3,x, algorithm="fricas")

[Out]

1/8*(20*x + 1)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.213973, size = 14, normalized size = 0.78 \[ \frac{20 x + 1}{32 x^{2} - 32 x + 8} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3+5*x)/(1-2*x)**3,x)

[Out]

(20*x + 1)/(32*x**2 - 32*x + 8)

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GIAC/XCAS [A]  time = 0.201467, size = 19, normalized size = 1.06 \[ \frac{20 \, x + 1}{8 \,{\left (2 \, x - 1\right )}^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)/(2*x - 1)^3,x, algorithm="giac")

[Out]

1/8*(20*x + 1)/(2*x - 1)^2