3.1212 \(\int \frac{1-2 x}{(3+5 x)^3} \, dx\)

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

[Out]

-(1 - 2*x)^2/(22*(3 + 5*x)^2)

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Rubi [A]  time = 0.0104842, 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 \[ -\frac{(1-2 x)^2}{22 (5 x+3)^2} \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)/(3 + 5*x)^3,x]

[Out]

-(1 - 2*x)^2/(22*(3 + 5*x)^2)

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Rubi in Sympy [A]  time = 2.48084, size = 15, normalized size = 0.83 \[ - \frac{\left (- 2 x + 1\right )^{2}}{22 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(-2*x + 1)**2/(22*(5*x + 3)**2)

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Mathematica [A]  time = 0.00424329, size = 16, normalized size = 0.89 \[ \frac{20 x+1}{50 (5 x+3)^2} \]

Antiderivative was successfully verified.

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

[Out]

(1 + 20*x)/(50*(3 + 5*x)^2)

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Maple [A]  time = 0.007, size = 20, normalized size = 1.1 \[ -{\frac{11}{50\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{2}{75+125\,x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)/(3+5*x)^3,x)

[Out]

-11/50/(3+5*x)^2+2/25/(3+5*x)

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Maxima [A]  time = 1.35034, size = 26, normalized size = 1.44 \[ \frac{20 \, x + 1}{50 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/50*(20*x + 1)/(25*x^2 + 30*x + 9)

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Fricas [A]  time = 0.22509, size = 26, normalized size = 1.44 \[ \frac{20 \, x + 1}{50 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/50*(20*x + 1)/(25*x^2 + 30*x + 9)

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Sympy [A]  time = 0.200825, size = 14, normalized size = 0.78 \[ \frac{20 x + 1}{1250 x^{2} + 1500 x + 450} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)/(3+5*x)**3,x)

[Out]

(20*x + 1)/(1250*x**2 + 1500*x + 450)

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GIAC/XCAS [A]  time = 0.207788, size = 19, normalized size = 1.06 \[ \frac{20 \, x + 1}{50 \,{\left (5 \, x + 3\right )}^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/50*(20*x + 1)/(5*x + 3)^2