3.1843 \(\int (1-2 x)^{3/2} (2+3 x)^3 (3+5 x) \, dx\)

Optimal. Leaf size=66 \[ -\frac{135}{208} (1-2 x)^{13/2}+\frac{621}{88} (1-2 x)^{11/2}-\frac{119}{4} (1-2 x)^{9/2}+\frac{469}{8} (1-2 x)^{7/2}-\frac{3773}{80} (1-2 x)^{5/2} \]

[Out]

(-3773*(1 - 2*x)^(5/2))/80 + (469*(1 - 2*x)^(7/2))/8 - (119*(1 - 2*x)^(9/2))/4 +
(621*(1 - 2*x)^(11/2))/88 - (135*(1 - 2*x)^(13/2))/208

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Rubi [A]  time = 0.0503384, antiderivative size = 66, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{135}{208} (1-2 x)^{13/2}+\frac{621}{88} (1-2 x)^{11/2}-\frac{119}{4} (1-2 x)^{9/2}+\frac{469}{8} (1-2 x)^{7/2}-\frac{3773}{80} (1-2 x)^{5/2} \]

Antiderivative was successfully verified.

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

[Out]

(-3773*(1 - 2*x)^(5/2))/80 + (469*(1 - 2*x)^(7/2))/8 - (119*(1 - 2*x)^(9/2))/4 +
(621*(1 - 2*x)^(11/2))/88 - (135*(1 - 2*x)^(13/2))/208

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Rubi in Sympy [A]  time = 8.22283, size = 58, normalized size = 0.88 \[ - \frac{135 \left (- 2 x + 1\right )^{\frac{13}{2}}}{208} + \frac{621 \left (- 2 x + 1\right )^{\frac{11}{2}}}{88} - \frac{119 \left (- 2 x + 1\right )^{\frac{9}{2}}}{4} + \frac{469 \left (- 2 x + 1\right )^{\frac{7}{2}}}{8} - \frac{3773 \left (- 2 x + 1\right )^{\frac{5}{2}}}{80} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135*(-2*x + 1)**(13/2)/208 + 621*(-2*x + 1)**(11/2)/88 - 119*(-2*x + 1)**(9/2)/
4 + 469*(-2*x + 1)**(7/2)/8 - 3773*(-2*x + 1)**(5/2)/80

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Mathematica [A]  time = 0.0395662, size = 33, normalized size = 0.5 \[ -\frac{1}{715} (1-2 x)^{5/2} \left (7425 x^4+25515 x^3+35675 x^2+25310 x+8494\right ) \]

Antiderivative was successfully verified.

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

[Out]

-((1 - 2*x)^(5/2)*(8494 + 25310*x + 35675*x^2 + 25515*x^3 + 7425*x^4))/715

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Maple [A]  time = 0.006, size = 30, normalized size = 0.5 \[ -{\frac{7425\,{x}^{4}+25515\,{x}^{3}+35675\,{x}^{2}+25310\,x+8494}{715} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/715*(7425*x^4+25515*x^3+35675*x^2+25310*x+8494)*(1-2*x)^(5/2)

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Maxima [A]  time = 1.35344, size = 62, normalized size = 0.94 \[ -\frac{135}{208} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} + \frac{621}{88} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{119}{4} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{469}{8} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{3773}{80} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135/208*(-2*x + 1)^(13/2) + 621/88*(-2*x + 1)^(11/2) - 119/4*(-2*x + 1)^(9/2) +
469/8*(-2*x + 1)^(7/2) - 3773/80*(-2*x + 1)^(5/2)

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Fricas [A]  time = 0.209094, size = 53, normalized size = 0.8 \[ -\frac{1}{715} \,{\left (29700 \, x^{6} + 72360 \, x^{5} + 48065 \, x^{4} - 15945 \, x^{3} - 31589 \, x^{2} - 8666 \, x + 8494\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/715*(29700*x^6 + 72360*x^5 + 48065*x^4 - 15945*x^3 - 31589*x^2 - 8666*x + 849
4)*sqrt(-2*x + 1)

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Sympy [A]  time = 6.43758, size = 58, normalized size = 0.88 \[ - \frac{135 \left (- 2 x + 1\right )^{\frac{13}{2}}}{208} + \frac{621 \left (- 2 x + 1\right )^{\frac{11}{2}}}{88} - \frac{119 \left (- 2 x + 1\right )^{\frac{9}{2}}}{4} + \frac{469 \left (- 2 x + 1\right )^{\frac{7}{2}}}{8} - \frac{3773 \left (- 2 x + 1\right )^{\frac{5}{2}}}{80} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135*(-2*x + 1)**(13/2)/208 + 621*(-2*x + 1)**(11/2)/88 - 119*(-2*x + 1)**(9/2)/
4 + 469*(-2*x + 1)**(7/2)/8 - 3773*(-2*x + 1)**(5/2)/80

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GIAC/XCAS [A]  time = 0.210532, size = 109, normalized size = 1.65 \[ -\frac{135}{208} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} - \frac{621}{88} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{119}{4} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{469}{8} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{3773}{80} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135/208*(2*x - 1)^6*sqrt(-2*x + 1) - 621/88*(2*x - 1)^5*sqrt(-2*x + 1) - 119/4*
(2*x - 1)^4*sqrt(-2*x + 1) - 469/8*(2*x - 1)^3*sqrt(-2*x + 1) - 3773/80*(2*x - 1
)^2*sqrt(-2*x + 1)