3.1927 \(\int (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^2 \, dx\)

Optimal. Leaf size=66 \[ -\frac{15}{16} (1-2 x)^{15/2}+\frac{255}{26} (1-2 x)^{13/2}-\frac{3467}{88} (1-2 x)^{11/2}+\frac{1309}{18} (1-2 x)^{9/2}-\frac{847}{16} (1-2 x)^{7/2} \]

[Out]

(-847*(1 - 2*x)^(7/2))/16 + (1309*(1 - 2*x)^(9/2))/18 - (3467*(1 - 2*x)^(11/2))/
88 + (255*(1 - 2*x)^(13/2))/26 - (15*(1 - 2*x)^(15/2))/16

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Rubi [A]  time = 0.064587, 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 \[ -\frac{15}{16} (1-2 x)^{15/2}+\frac{255}{26} (1-2 x)^{13/2}-\frac{3467}{88} (1-2 x)^{11/2}+\frac{1309}{18} (1-2 x)^{9/2}-\frac{847}{16} (1-2 x)^{7/2} \]

Antiderivative was successfully verified.

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

[Out]

(-847*(1 - 2*x)^(7/2))/16 + (1309*(1 - 2*x)^(9/2))/18 - (3467*(1 - 2*x)^(11/2))/
88 + (255*(1 - 2*x)^(13/2))/26 - (15*(1 - 2*x)^(15/2))/16

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Rubi in Sympy [A]  time = 8.46977, size = 58, normalized size = 0.88 \[ - \frac{15 \left (- 2 x + 1\right )^{\frac{15}{2}}}{16} + \frac{255 \left (- 2 x + 1\right )^{\frac{13}{2}}}{26} - \frac{3467 \left (- 2 x + 1\right )^{\frac{11}{2}}}{88} + \frac{1309 \left (- 2 x + 1\right )^{\frac{9}{2}}}{18} - \frac{847 \left (- 2 x + 1\right )^{\frac{7}{2}}}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15*(-2*x + 1)**(15/2)/16 + 255*(-2*x + 1)**(13/2)/26 - 3467*(-2*x + 1)**(11/2)/
88 + 1309*(-2*x + 1)**(9/2)/18 - 847*(-2*x + 1)**(7/2)/16

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Mathematica [A]  time = 0.053234, size = 33, normalized size = 0.5 \[ -\frac{(1-2 x)^{7/2} \left (19305 x^4+62370 x^3+80307 x^2+50450 x+13826\right )}{1287} \]

Antiderivative was successfully verified.

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

[Out]

-((1 - 2*x)^(7/2)*(13826 + 50450*x + 80307*x^2 + 62370*x^3 + 19305*x^4))/1287

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Maple [A]  time = 0.005, size = 30, normalized size = 0.5 \[ -{\frac{19305\,{x}^{4}+62370\,{x}^{3}+80307\,{x}^{2}+50450\,x+13826}{1287} \left ( 1-2\,x \right ) ^{{\frac{7}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/1287*(19305*x^4+62370*x^3+80307*x^2+50450*x+13826)*(1-2*x)^(7/2)

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Maxima [A]  time = 1.33029, size = 62, normalized size = 0.94 \[ -\frac{15}{16} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{255}{26} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{3467}{88} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{1309}{18} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{847}{16} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15/16*(-2*x + 1)^(15/2) + 255/26*(-2*x + 1)^(13/2) - 3467/88*(-2*x + 1)^(11/2)
+ 1309/18*(-2*x + 1)^(9/2) - 847/16*(-2*x + 1)^(7/2)

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Fricas [A]  time = 0.235843, size = 59, normalized size = 0.89 \[ \frac{1}{1287} \,{\left (154440 \, x^{7} + 267300 \, x^{6} + 9846 \, x^{5} - 205169 \, x^{4} - 75320 \, x^{3} + 56481 \, x^{2} + 32506 \, x - 13826\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1287*(154440*x^7 + 267300*x^6 + 9846*x^5 - 205169*x^4 - 75320*x^3 + 56481*x^2
+ 32506*x - 13826)*sqrt(-2*x + 1)

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Sympy [A]  time = 4.38694, size = 58, normalized size = 0.88 \[ - \frac{15 \left (- 2 x + 1\right )^{\frac{15}{2}}}{16} + \frac{255 \left (- 2 x + 1\right )^{\frac{13}{2}}}{26} - \frac{3467 \left (- 2 x + 1\right )^{\frac{11}{2}}}{88} + \frac{1309 \left (- 2 x + 1\right )^{\frac{9}{2}}}{18} - \frac{847 \left (- 2 x + 1\right )^{\frac{7}{2}}}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15*(-2*x + 1)**(15/2)/16 + 255*(-2*x + 1)**(13/2)/26 - 3467*(-2*x + 1)**(11/2)/
88 + 1309*(-2*x + 1)**(9/2)/18 - 847*(-2*x + 1)**(7/2)/16

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GIAC/XCAS [A]  time = 0.213177, size = 109, normalized size = 1.65 \[ \frac{15}{16} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} + \frac{255}{26} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{3467}{88} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{1309}{18} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{847}{16} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

15/16*(2*x - 1)^7*sqrt(-2*x + 1) + 255/26*(2*x - 1)^6*sqrt(-2*x + 1) + 3467/88*(
2*x - 1)^5*sqrt(-2*x + 1) + 1309/18*(2*x - 1)^4*sqrt(-2*x + 1) + 847/16*(2*x - 1
)^3*sqrt(-2*x + 1)