3.1940 \(\int (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^3 \, dx\)

Optimal. Leaf size=79 \[ \frac{1125}{544} (1-2 x)^{17/2}-\frac{845}{32} (1-2 x)^{15/2}+\frac{28555}{208} (1-2 x)^{13/2}-\frac{5847}{16} (1-2 x)^{11/2}+\frac{16093}{32} (1-2 x)^{9/2}-\frac{9317}{32} (1-2 x)^{7/2} \]

[Out]

(-9317*(1 - 2*x)^(7/2))/32 + (16093*(1 - 2*x)^(9/2))/32 - (5847*(1 - 2*x)^(11/2)
)/16 + (28555*(1 - 2*x)^(13/2))/208 - (845*(1 - 2*x)^(15/2))/32 + (1125*(1 - 2*x
)^(17/2))/544

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Rubi [A]  time = 0.0702132, antiderivative size = 79, 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 \[ \frac{1125}{544} (1-2 x)^{17/2}-\frac{845}{32} (1-2 x)^{15/2}+\frac{28555}{208} (1-2 x)^{13/2}-\frac{5847}{16} (1-2 x)^{11/2}+\frac{16093}{32} (1-2 x)^{9/2}-\frac{9317}{32} (1-2 x)^{7/2} \]

Antiderivative was successfully verified.

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

[Out]

(-9317*(1 - 2*x)^(7/2))/32 + (16093*(1 - 2*x)^(9/2))/32 - (5847*(1 - 2*x)^(11/2)
)/16 + (28555*(1 - 2*x)^(13/2))/208 - (845*(1 - 2*x)^(15/2))/32 + (1125*(1 - 2*x
)^(17/2))/544

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Rubi in Sympy [A]  time = 9.48245, size = 70, normalized size = 0.89 \[ \frac{1125 \left (- 2 x + 1\right )^{\frac{17}{2}}}{544} - \frac{845 \left (- 2 x + 1\right )^{\frac{15}{2}}}{32} + \frac{28555 \left (- 2 x + 1\right )^{\frac{13}{2}}}{208} - \frac{5847 \left (- 2 x + 1\right )^{\frac{11}{2}}}{16} + \frac{16093 \left (- 2 x + 1\right )^{\frac{9}{2}}}{32} - \frac{9317 \left (- 2 x + 1\right )^{\frac{7}{2}}}{32} \]

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)**3,x)

[Out]

1125*(-2*x + 1)**(17/2)/544 - 845*(-2*x + 1)**(15/2)/32 + 28555*(-2*x + 1)**(13/
2)/208 - 5847*(-2*x + 1)**(11/2)/16 + 16093*(-2*x + 1)**(9/2)/32 - 9317*(-2*x +
1)**(7/2)/32

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Mathematica [A]  time = 0.0557228, size = 38, normalized size = 0.48 \[ -\frac{1}{221} (1-2 x)^{7/2} \left (14625 x^5+56810 x^4+92535 x^3+80748 x^2+39160 x+9004\right ) \]

Antiderivative was successfully verified.

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

[Out]

-((1 - 2*x)^(7/2)*(9004 + 39160*x + 80748*x^2 + 92535*x^3 + 56810*x^4 + 14625*x^
5))/221

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Maple [A]  time = 0.006, size = 35, normalized size = 0.4 \[ -{\frac{14625\,{x}^{5}+56810\,{x}^{4}+92535\,{x}^{3}+80748\,{x}^{2}+39160\,x+9004}{221} \left ( 1-2\,x \right ) ^{{\frac{7}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/221*(14625*x^5+56810*x^4+92535*x^3+80748*x^2+39160*x+9004)*(1-2*x)^(7/2)

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Maxima [A]  time = 1.35608, size = 74, normalized size = 0.94 \[ \frac{1125}{544} \,{\left (-2 \, x + 1\right )}^{\frac{17}{2}} - \frac{845}{32} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{28555}{208} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{5847}{16} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{16093}{32} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{9317}{32} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1125/544*(-2*x + 1)^(17/2) - 845/32*(-2*x + 1)^(15/2) + 28555/208*(-2*x + 1)^(13
/2) - 5847/16*(-2*x + 1)^(11/2) + 16093/32*(-2*x + 1)^(9/2) - 9317/32*(-2*x + 1)
^(7/2)

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Fricas [A]  time = 0.206102, size = 66, normalized size = 0.84 \[ \frac{1}{221} \,{\left (117000 \, x^{8} + 278980 \, x^{7} + 146310 \, x^{6} - 138201 \, x^{5} - 157296 \, x^{4} - 5935 \, x^{3} + 46164 \, x^{2} + 14864 \, x - 9004\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/221*(117000*x^8 + 278980*x^7 + 146310*x^6 - 138201*x^5 - 157296*x^4 - 5935*x^3
+ 46164*x^2 + 14864*x - 9004)*sqrt(-2*x + 1)

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Sympy [A]  time = 4.98225, size = 70, normalized size = 0.89 \[ \frac{1125 \left (- 2 x + 1\right )^{\frac{17}{2}}}{544} - \frac{845 \left (- 2 x + 1\right )^{\frac{15}{2}}}{32} + \frac{28555 \left (- 2 x + 1\right )^{\frac{13}{2}}}{208} - \frac{5847 \left (- 2 x + 1\right )^{\frac{11}{2}}}{16} + \frac{16093 \left (- 2 x + 1\right )^{\frac{9}{2}}}{32} - \frac{9317 \left (- 2 x + 1\right )^{\frac{7}{2}}}{32} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1125*(-2*x + 1)**(17/2)/544 - 845*(-2*x + 1)**(15/2)/32 + 28555*(-2*x + 1)**(13/
2)/208 - 5847*(-2*x + 1)**(11/2)/16 + 16093*(-2*x + 1)**(9/2)/32 - 9317*(-2*x +
1)**(7/2)/32

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GIAC/XCAS [A]  time = 0.218469, size = 131, normalized size = 1.66 \[ \frac{1125}{544} \,{\left (2 \, x - 1\right )}^{8} \sqrt{-2 \, x + 1} + \frac{845}{32} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} + \frac{28555}{208} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{5847}{16} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{16093}{32} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{9317}{32} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1125/544*(2*x - 1)^8*sqrt(-2*x + 1) + 845/32*(2*x - 1)^7*sqrt(-2*x + 1) + 28555/
208*(2*x - 1)^6*sqrt(-2*x + 1) + 5847/16*(2*x - 1)^5*sqrt(-2*x + 1) + 16093/32*(
2*x - 1)^4*sqrt(-2*x + 1) + 9317/32*(2*x - 1)^3*sqrt(-2*x + 1)