3.2069 \(\int \frac{(2+3 x)^2 (3+5 x)^2}{(1-2 x)^{3/2}} \, dx\)

Optimal. Leaf size=66 \[ -\frac{225}{112} (1-2 x)^{7/2}+\frac{51}{2} (1-2 x)^{5/2}-\frac{3467}{24} (1-2 x)^{3/2}+\frac{1309}{2} \sqrt{1-2 x}+\frac{5929}{16 \sqrt{1-2 x}} \]

[Out]

5929/(16*Sqrt[1 - 2*x]) + (1309*Sqrt[1 - 2*x])/2 - (3467*(1 - 2*x)^(3/2))/24 + (
51*(1 - 2*x)^(5/2))/2 - (225*(1 - 2*x)^(7/2))/112

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Rubi [A]  time = 0.0619145, antiderivative size = 66, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ -\frac{225}{112} (1-2 x)^{7/2}+\frac{51}{2} (1-2 x)^{5/2}-\frac{3467}{24} (1-2 x)^{3/2}+\frac{1309}{2} \sqrt{1-2 x}+\frac{5929}{16 \sqrt{1-2 x}} \]

Antiderivative was successfully verified.

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

[Out]

5929/(16*Sqrt[1 - 2*x]) + (1309*Sqrt[1 - 2*x])/2 - (3467*(1 - 2*x)^(3/2))/24 + (
51*(1 - 2*x)^(5/2))/2 - (225*(1 - 2*x)^(7/2))/112

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Rubi in Sympy [A]  time = 8.84576, size = 58, normalized size = 0.88 \[ - \frac{225 \left (- 2 x + 1\right )^{\frac{7}{2}}}{112} + \frac{51 \left (- 2 x + 1\right )^{\frac{5}{2}}}{2} - \frac{3467 \left (- 2 x + 1\right )^{\frac{3}{2}}}{24} + \frac{1309 \sqrt{- 2 x + 1}}{2} + \frac{5929}{16 \sqrt{- 2 x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225*(-2*x + 1)**(7/2)/112 + 51*(-2*x + 1)**(5/2)/2 - 3467*(-2*x + 1)**(3/2)/24
+ 1309*sqrt(-2*x + 1)/2 + 5929/(16*sqrt(-2*x + 1))

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Mathematica [A]  time = 0.0502549, size = 33, normalized size = 0.5 \[ \frac{-675 x^4-2934 x^3-6721 x^2-18230 x+18986}{21 \sqrt{1-2 x}} \]

Antiderivative was successfully verified.

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

[Out]

(18986 - 18230*x - 6721*x^2 - 2934*x^3 - 675*x^4)/(21*Sqrt[1 - 2*x])

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Maple [A]  time = 0.006, size = 30, normalized size = 0.5 \[ -{\frac{675\,{x}^{4}+2934\,{x}^{3}+6721\,{x}^{2}+18230\,x-18986}{21}{\frac{1}{\sqrt{1-2\,x}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/21*(675*x^4+2934*x^3+6721*x^2+18230*x-18986)/(1-2*x)^(1/2)

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Maxima [A]  time = 1.34079, size = 62, normalized size = 0.94 \[ -\frac{225}{112} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{51}{2} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{3467}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{1309}{2} \, \sqrt{-2 \, x + 1} + \frac{5929}{16 \, \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225/112*(-2*x + 1)^(7/2) + 51/2*(-2*x + 1)^(5/2) - 3467/24*(-2*x + 1)^(3/2) + 1
309/2*sqrt(-2*x + 1) + 5929/16/sqrt(-2*x + 1)

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Fricas [A]  time = 0.216797, size = 39, normalized size = 0.59 \[ -\frac{675 \, x^{4} + 2934 \, x^{3} + 6721 \, x^{2} + 18230 \, x - 18986}{21 \, \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/21*(675*x^4 + 2934*x^3 + 6721*x^2 + 18230*x - 18986)/sqrt(-2*x + 1)

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Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (3 x + 2\right )^{2} \left (5 x + 3\right )^{2}}{\left (- 2 x + 1\right )^{\frac{3}{2}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Integral((3*x + 2)**2*(5*x + 3)**2/(-2*x + 1)**(3/2), x)

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GIAC/XCAS [A]  time = 0.216828, size = 81, normalized size = 1.23 \[ \frac{225}{112} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{51}{2} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{3467}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{1309}{2} \, \sqrt{-2 \, x + 1} + \frac{5929}{16 \, \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

225/112*(2*x - 1)^3*sqrt(-2*x + 1) + 51/2*(2*x - 1)^2*sqrt(-2*x + 1) - 3467/24*(
-2*x + 1)^(3/2) + 1309/2*sqrt(-2*x + 1) + 5929/16/sqrt(-2*x + 1)