3.2134 \(\int \frac{(3+5 x)^2}{(1-2 x)^{5/2}} \, dx\)

Optimal. Leaf size=40 \[ -\frac{25}{4} \sqrt{1-2 x}-\frac{55}{2 \sqrt{1-2 x}}+\frac{121}{12 (1-2 x)^{3/2}} \]

[Out]

121/(12*(1 - 2*x)^(3/2)) - 55/(2*Sqrt[1 - 2*x]) - (25*Sqrt[1 - 2*x])/4

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Rubi [A]  time = 0.0297779, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ -\frac{25}{4} \sqrt{1-2 x}-\frac{55}{2 \sqrt{1-2 x}}+\frac{121}{12 (1-2 x)^{3/2}} \]

Antiderivative was successfully verified.

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

[Out]

121/(12*(1 - 2*x)^(3/2)) - 55/(2*Sqrt[1 - 2*x]) - (25*Sqrt[1 - 2*x])/4

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Rubi in Sympy [A]  time = 5.1189, size = 34, normalized size = 0.85 \[ - \frac{25 \sqrt{- 2 x + 1}}{4} - \frac{55}{2 \sqrt{- 2 x + 1}} + \frac{121}{12 \left (- 2 x + 1\right )^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25*sqrt(-2*x + 1)/4 - 55/(2*sqrt(-2*x + 1)) + 121/(12*(-2*x + 1)**(3/2))

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Mathematica [A]  time = 0.0285201, size = 23, normalized size = 0.57 \[ \frac{-75 x^2+240 x-71}{3 (1-2 x)^{3/2}} \]

Antiderivative was successfully verified.

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

[Out]

(-71 + 240*x - 75*x^2)/(3*(1 - 2*x)^(3/2))

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Maple [A]  time = 0.004, size = 20, normalized size = 0.5 \[ -{\frac{75\,{x}^{2}-240\,x+71}{3} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+5*x)^2/(1-2*x)^(5/2),x)

[Out]

-1/3*(75*x^2-240*x+71)/(1-2*x)^(3/2)

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Maxima [A]  time = 1.33272, size = 32, normalized size = 0.8 \[ -\frac{25}{4} \, \sqrt{-2 \, x + 1} + \frac{11 \,{\left (60 \, x - 19\right )}}{12 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/4*sqrt(-2*x + 1) + 11/12*(60*x - 19)/(-2*x + 1)^(3/2)

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Fricas [A]  time = 0.21317, size = 35, normalized size = 0.88 \[ \frac{75 \, x^{2} - 240 \, x + 71}{3 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*(75*x^2 - 240*x + 71)/((2*x - 1)*sqrt(-2*x + 1))

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Sympy [A]  time = 1.11617, size = 75, normalized size = 1.88 \[ \frac{75 x^{2}}{6 x \sqrt{- 2 x + 1} - 3 \sqrt{- 2 x + 1}} - \frac{240 x}{6 x \sqrt{- 2 x + 1} - 3 \sqrt{- 2 x + 1}} + \frac{71}{6 x \sqrt{- 2 x + 1} - 3 \sqrt{- 2 x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

75*x**2/(6*x*sqrt(-2*x + 1) - 3*sqrt(-2*x + 1)) - 240*x/(6*x*sqrt(-2*x + 1) - 3*
sqrt(-2*x + 1)) + 71/(6*x*sqrt(-2*x + 1) - 3*sqrt(-2*x + 1))

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GIAC/XCAS [A]  time = 0.209473, size = 42, normalized size = 1.05 \[ -\frac{25}{4} \, \sqrt{-2 \, x + 1} - \frac{11 \,{\left (60 \, x - 19\right )}}{12 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/4*sqrt(-2*x + 1) - 11/12*(60*x - 19)/((2*x - 1)*sqrt(-2*x + 1))