3.49 \(\int \frac{3+2 x}{(7+6 x)^3} \, dx\)

Optimal. Leaf size=18 \[ -\frac{(2 x+3)^2}{8 (6 x+7)^2} \]

[Out]

-(3 + 2*x)^2/(8*(7 + 6*x)^2)

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Rubi [A]  time = 0.00943694, 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 \[ -\frac{(2 x+3)^2}{8 (6 x+7)^2} \]

Antiderivative was successfully verified.

[In]  Int[(3 + 2*x)/(7 + 6*x)^3,x]

[Out]

-(3 + 2*x)^2/(8*(7 + 6*x)^2)

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Rubi in Sympy [A]  time = 1.13854, size = 15, normalized size = 0.83 \[ - \frac{\left (2 x + 3\right )^{2}}{8 \left (6 x + 7\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((3+2*x)/(7+6*x)**3,x)

[Out]

-(2*x + 3)**2/(8*(6*x + 7)**2)

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Mathematica [A]  time = 0.00576289, size = 16, normalized size = 0.89 \[ -\frac{3 x+4}{9 (6 x+7)^2} \]

Antiderivative was successfully verified.

[In]  Integrate[(3 + 2*x)/(7 + 6*x)^3,x]

[Out]

-(4 + 3*x)/(9*(7 + 6*x)^2)

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Maple [A]  time = 0.01, size = 20, normalized size = 1.1 \[ -{\frac{1}{126+108\,x}}-{\frac{1}{18\, \left ( 7+6\,x \right ) ^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+2*x)/(7+6*x)^3,x)

[Out]

-1/18/(7+6*x)-1/18/(7+6*x)^2

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Maxima [A]  time = 1.35996, size = 26, normalized size = 1.44 \[ -\frac{3 \, x + 4}{9 \,{\left (36 \, x^{2} + 84 \, x + 49\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x + 3)/(6*x + 7)^3,x, algorithm="maxima")

[Out]

-1/9*(3*x + 4)/(36*x^2 + 84*x + 49)

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Fricas [A]  time = 0.189883, size = 26, normalized size = 1.44 \[ -\frac{3 \, x + 4}{9 \,{\left (36 \, x^{2} + 84 \, x + 49\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x + 3)/(6*x + 7)^3,x, algorithm="fricas")

[Out]

-1/9*(3*x + 4)/(36*x^2 + 84*x + 49)

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Sympy [A]  time = 0.102592, size = 15, normalized size = 0.83 \[ - \frac{3 x + 4}{324 x^{2} + 756 x + 441} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3+2*x)/(7+6*x)**3,x)

[Out]

-(3*x + 4)/(324*x**2 + 756*x + 441)

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GIAC/XCAS [A]  time = 0.214813, size = 19, normalized size = 1.06 \[ -\frac{3 \, x + 4}{9 \,{\left (6 \, x + 7\right )}^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x + 3)/(6*x + 7)^3,x, algorithm="giac")

[Out]

-1/9*(3*x + 4)/(6*x + 7)^2