3.1788 \(\int \sqrt{1-2 x} (2+3 x)^2 (3+5 x)^2 \, dx\)

Optimal. Leaf size=66 \[ -\frac{225}{176} (1-2 x)^{11/2}+\frac{85}{6} (1-2 x)^{9/2}-\frac{3467}{56} (1-2 x)^{7/2}+\frac{1309}{10} (1-2 x)^{5/2}-\frac{5929}{48} (1-2 x)^{3/2} \]

[Out]

(-5929*(1 - 2*x)^(3/2))/48 + (1309*(1 - 2*x)^(5/2))/10 - (3467*(1 - 2*x)^(7/2))/
56 + (85*(1 - 2*x)^(9/2))/6 - (225*(1 - 2*x)^(11/2))/176

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Rubi [A]  time = 0.0555836, 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 \[ -\frac{225}{176} (1-2 x)^{11/2}+\frac{85}{6} (1-2 x)^{9/2}-\frac{3467}{56} (1-2 x)^{7/2}+\frac{1309}{10} (1-2 x)^{5/2}-\frac{5929}{48} (1-2 x)^{3/2} \]

Antiderivative was successfully verified.

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

[Out]

(-5929*(1 - 2*x)^(3/2))/48 + (1309*(1 - 2*x)^(5/2))/10 - (3467*(1 - 2*x)^(7/2))/
56 + (85*(1 - 2*x)^(9/2))/6 - (225*(1 - 2*x)^(11/2))/176

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Rubi in Sympy [A]  time = 8.36407, size = 58, normalized size = 0.88 \[ - \frac{225 \left (- 2 x + 1\right )^{\frac{11}{2}}}{176} + \frac{85 \left (- 2 x + 1\right )^{\frac{9}{2}}}{6} - \frac{3467 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} + \frac{1309 \left (- 2 x + 1\right )^{\frac{5}{2}}}{10} - \frac{5929 \left (- 2 x + 1\right )^{\frac{3}{2}}}{48} \]

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]

-225*(-2*x + 1)**(11/2)/176 + 85*(-2*x + 1)**(9/2)/6 - 3467*(-2*x + 1)**(7/2)/56
+ 1309*(-2*x + 1)**(5/2)/10 - 5929*(-2*x + 1)**(3/2)/48

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Mathematica [A]  time = 0.0516299, size = 33, normalized size = 0.5 \[ -\frac{(1-2 x)^{3/2} \left (23625 x^4+83650 x^3+125115 x^2+102714 x+48098\right )}{1155} \]

Antiderivative was successfully verified.

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

[Out]

-((1 - 2*x)^(3/2)*(48098 + 102714*x + 125115*x^2 + 83650*x^3 + 23625*x^4))/1155

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Maple [A]  time = 0.007, size = 30, normalized size = 0.5 \[ -{\frac{23625\,{x}^{4}+83650\,{x}^{3}+125115\,{x}^{2}+102714\,x+48098}{1155} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}} \]

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]

-1/1155*(23625*x^4+83650*x^3+125115*x^2+102714*x+48098)*(1-2*x)^(3/2)

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Maxima [A]  time = 1.34646, size = 62, normalized size = 0.94 \[ -\frac{225}{176} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{85}{6} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{3467}{56} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{1309}{10} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{5929}{48} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]

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]

-225/176*(-2*x + 1)^(11/2) + 85/6*(-2*x + 1)^(9/2) - 3467/56*(-2*x + 1)^(7/2) +
1309/10*(-2*x + 1)^(5/2) - 5929/48*(-2*x + 1)^(3/2)

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Fricas [A]  time = 0.211954, size = 46, normalized size = 0.7 \[ \frac{1}{1155} \,{\left (47250 \, x^{5} + 143675 \, x^{4} + 166580 \, x^{3} + 80313 \, x^{2} - 6518 \, x - 48098\right )} \sqrt{-2 \, x + 1} \]

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]

1/1155*(47250*x^5 + 143675*x^4 + 166580*x^3 + 80313*x^2 - 6518*x - 48098)*sqrt(-
2*x + 1)

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Sympy [A]  time = 2.96689, size = 58, normalized size = 0.88 \[ - \frac{225 \left (- 2 x + 1\right )^{\frac{11}{2}}}{176} + \frac{85 \left (- 2 x + 1\right )^{\frac{9}{2}}}{6} - \frac{3467 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} + \frac{1309 \left (- 2 x + 1\right )^{\frac{5}{2}}}{10} - \frac{5929 \left (- 2 x + 1\right )^{\frac{3}{2}}}{48} \]

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]

-225*(-2*x + 1)**(11/2)/176 + 85*(-2*x + 1)**(9/2)/6 - 3467*(-2*x + 1)**(7/2)/56
+ 1309*(-2*x + 1)**(5/2)/10 - 5929*(-2*x + 1)**(3/2)/48

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GIAC/XCAS [A]  time = 0.211629, size = 100, normalized size = 1.52 \[ \frac{225}{176} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{85}{6} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{3467}{56} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{1309}{10} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{5929}{48} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]

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]

225/176*(2*x - 1)^5*sqrt(-2*x + 1) + 85/6*(2*x - 1)^4*sqrt(-2*x + 1) + 3467/56*(
2*x - 1)^3*sqrt(-2*x + 1) + 1309/10*(2*x - 1)^2*sqrt(-2*x + 1) - 5929/48*(-2*x +
1)^(3/2)