3.1998 \(\int \frac{(2+3 x)^2 (3+5 x)^2}{\sqrt{1-2 x}} \, dx\)

Optimal. Leaf size=66 \[ -\frac{25}{16} (1-2 x)^{9/2}+\frac{255}{14} (1-2 x)^{7/2}-\frac{3467}{40} (1-2 x)^{5/2}+\frac{1309}{6} (1-2 x)^{3/2}-\frac{5929}{16} \sqrt{1-2 x} \]

[Out]

(-5929*Sqrt[1 - 2*x])/16 + (1309*(1 - 2*x)^(3/2))/6 - (3467*(1 - 2*x)^(5/2))/40
+ (255*(1 - 2*x)^(7/2))/14 - (25*(1 - 2*x)^(9/2))/16

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Rubi [A]  time = 0.0639656, 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 \[ -\frac{25}{16} (1-2 x)^{9/2}+\frac{255}{14} (1-2 x)^{7/2}-\frac{3467}{40} (1-2 x)^{5/2}+\frac{1309}{6} (1-2 x)^{3/2}-\frac{5929}{16} \sqrt{1-2 x} \]

Antiderivative was successfully verified.

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

[Out]

(-5929*Sqrt[1 - 2*x])/16 + (1309*(1 - 2*x)^(3/2))/6 - (3467*(1 - 2*x)^(5/2))/40
+ (255*(1 - 2*x)^(7/2))/14 - (25*(1 - 2*x)^(9/2))/16

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Rubi in Sympy [A]  time = 8.39035, size = 58, normalized size = 0.88 \[ - \frac{25 \left (- 2 x + 1\right )^{\frac{9}{2}}}{16} + \frac{255 \left (- 2 x + 1\right )^{\frac{7}{2}}}{14} - \frac{3467 \left (- 2 x + 1\right )^{\frac{5}{2}}}{40} + \frac{1309 \left (- 2 x + 1\right )^{\frac{3}{2}}}{6} - \frac{5929 \sqrt{- 2 x + 1}}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25*(-2*x + 1)**(9/2)/16 + 255*(-2*x + 1)**(7/2)/14 - 3467*(-2*x + 1)**(5/2)/40
+ 1309*(-2*x + 1)**(3/2)/6 - 5929*sqrt(-2*x + 1)/16

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Mathematica [A]  time = 0.0457333, size = 33, normalized size = 0.5 \[ -\frac{1}{105} \sqrt{1-2 x} \left (2625 x^4+10050 x^3+17391 x^2+19574 x+23354\right ) \]

Antiderivative was successfully verified.

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

[Out]

-(Sqrt[1 - 2*x]*(23354 + 19574*x + 17391*x^2 + 10050*x^3 + 2625*x^4))/105

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Maple [A]  time = 0.006, size = 30, normalized size = 0.5 \[ -{\frac{2625\,{x}^{4}+10050\,{x}^{3}+17391\,{x}^{2}+19574\,x+23354}{105}\sqrt{1-2\,x}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/105*(2625*x^4+10050*x^3+17391*x^2+19574*x+23354)*(1-2*x)^(1/2)

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Maxima [A]  time = 1.34345, size = 62, normalized size = 0.94 \[ -\frac{25}{16} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{255}{14} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{3467}{40} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{1309}{6} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{5929}{16} \, \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/16*(-2*x + 1)^(9/2) + 255/14*(-2*x + 1)^(7/2) - 3467/40*(-2*x + 1)^(5/2) + 1
309/6*(-2*x + 1)^(3/2) - 5929/16*sqrt(-2*x + 1)

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Fricas [A]  time = 0.201366, size = 39, normalized size = 0.59 \[ -\frac{1}{105} \,{\left (2625 \, x^{4} + 10050 \, x^{3} + 17391 \, x^{2} + 19574 \, x + 23354\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/105*(2625*x^4 + 10050*x^3 + 17391*x^2 + 19574*x + 23354)*sqrt(-2*x + 1)

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Sympy [A]  time = 9.88765, size = 58, normalized size = 0.88 \[ - \frac{25 \left (- 2 x + 1\right )^{\frac{9}{2}}}{16} + \frac{255 \left (- 2 x + 1\right )^{\frac{7}{2}}}{14} - \frac{3467 \left (- 2 x + 1\right )^{\frac{5}{2}}}{40} + \frac{1309 \left (- 2 x + 1\right )^{\frac{3}{2}}}{6} - \frac{5929 \sqrt{- 2 x + 1}}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25*(-2*x + 1)**(9/2)/16 + 255*(-2*x + 1)**(7/2)/14 - 3467*(-2*x + 1)**(5/2)/40
+ 1309*(-2*x + 1)**(3/2)/6 - 5929*sqrt(-2*x + 1)/16

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GIAC/XCAS [A]  time = 0.211166, size = 90, normalized size = 1.36 \[ -\frac{25}{16} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{255}{14} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{3467}{40} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{1309}{6} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{5929}{16} \, \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/16*(2*x - 1)^4*sqrt(-2*x + 1) - 255/14*(2*x - 1)^3*sqrt(-2*x + 1) - 3467/40*
(2*x - 1)^2*sqrt(-2*x + 1) + 1309/6*(-2*x + 1)^(3/2) - 5929/16*sqrt(-2*x + 1)