3.1855 \(\int (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^2 \, dx\)

Optimal. Leaf size=66 \[ -\frac{225}{208} (1-2 x)^{13/2}+\frac{255}{22} (1-2 x)^{11/2}-\frac{3467}{72} (1-2 x)^{9/2}+\frac{187}{2} (1-2 x)^{7/2}-\frac{5929}{80} (1-2 x)^{5/2} \]

[Out]

(-5929*(1 - 2*x)^(5/2))/80 + (187*(1 - 2*x)^(7/2))/2 - (3467*(1 - 2*x)^(9/2))/72
+ (255*(1 - 2*x)^(11/2))/22 - (225*(1 - 2*x)^(13/2))/208

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Rubi [A]  time = 0.0587761, 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 \[ -\frac{225}{208} (1-2 x)^{13/2}+\frac{255}{22} (1-2 x)^{11/2}-\frac{3467}{72} (1-2 x)^{9/2}+\frac{187}{2} (1-2 x)^{7/2}-\frac{5929}{80} (1-2 x)^{5/2} \]

Antiderivative was successfully verified.

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

[Out]

(-5929*(1 - 2*x)^(5/2))/80 + (187*(1 - 2*x)^(7/2))/2 - (3467*(1 - 2*x)^(9/2))/72
+ (255*(1 - 2*x)^(11/2))/22 - (225*(1 - 2*x)^(13/2))/208

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Rubi in Sympy [A]  time = 8.8943, size = 58, normalized size = 0.88 \[ - \frac{225 \left (- 2 x + 1\right )^{\frac{13}{2}}}{208} + \frac{255 \left (- 2 x + 1\right )^{\frac{11}{2}}}{22} - \frac{3467 \left (- 2 x + 1\right )^{\frac{9}{2}}}{72} + \frac{187 \left (- 2 x + 1\right )^{\frac{7}{2}}}{2} - \frac{5929 \left (- 2 x + 1\right )^{\frac{5}{2}}}{80} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225*(-2*x + 1)**(13/2)/208 + 255*(-2*x + 1)**(11/2)/22 - 3467*(-2*x + 1)**(9/2)
/72 + 187*(-2*x + 1)**(7/2)/2 - 5929*(-2*x + 1)**(5/2)/80

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Mathematica [A]  time = 0.0505749, size = 33, normalized size = 0.5 \[ -\frac{(1-2 x)^{5/2} \left (111375 x^4+373950 x^3+511465 x^2+355730 x+117478\right )}{6435} \]

Antiderivative was successfully verified.

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

[Out]

-((1 - 2*x)^(5/2)*(117478 + 355730*x + 511465*x^2 + 373950*x^3 + 111375*x^4))/64
35

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Maple [A]  time = 0.007, size = 30, normalized size = 0.5 \[ -{\frac{111375\,{x}^{4}+373950\,{x}^{3}+511465\,{x}^{2}+355730\,x+117478}{6435} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6435*(111375*x^4+373950*x^3+511465*x^2+355730*x+117478)*(1-2*x)^(5/2)

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Maxima [A]  time = 1.34991, size = 62, normalized size = 0.94 \[ -\frac{225}{208} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} + \frac{255}{22} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{3467}{72} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{187}{2} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{5929}{80} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225/208*(-2*x + 1)^(13/2) + 255/22*(-2*x + 1)^(11/2) - 3467/72*(-2*x + 1)^(9/2)
+ 187/2*(-2*x + 1)^(7/2) - 5929/80*(-2*x + 1)^(5/2)

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Fricas [A]  time = 0.205361, size = 53, normalized size = 0.8 \[ -\frac{1}{6435} \,{\left (445500 \, x^{6} + 1050300 \, x^{5} + 661435 \, x^{4} - 248990 \, x^{3} - 441543 \, x^{2} - 114182 \, x + 117478\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6435*(445500*x^6 + 1050300*x^5 + 661435*x^4 - 248990*x^3 - 441543*x^2 - 11418
2*x + 117478)*sqrt(-2*x + 1)

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Sympy [A]  time = 3.09588, size = 58, normalized size = 0.88 \[ - \frac{225 \left (- 2 x + 1\right )^{\frac{13}{2}}}{208} + \frac{255 \left (- 2 x + 1\right )^{\frac{11}{2}}}{22} - \frac{3467 \left (- 2 x + 1\right )^{\frac{9}{2}}}{72} + \frac{187 \left (- 2 x + 1\right )^{\frac{7}{2}}}{2} - \frac{5929 \left (- 2 x + 1\right )^{\frac{5}{2}}}{80} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225*(-2*x + 1)**(13/2)/208 + 255*(-2*x + 1)**(11/2)/22 - 3467*(-2*x + 1)**(9/2)
/72 + 187*(-2*x + 1)**(7/2)/2 - 5929*(-2*x + 1)**(5/2)/80

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GIAC/XCAS [A]  time = 0.218878, size = 109, normalized size = 1.65 \[ -\frac{225}{208} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} - \frac{255}{22} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{3467}{72} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{187}{2} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{5929}{80} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225/208*(2*x - 1)^6*sqrt(-2*x + 1) - 255/22*(2*x - 1)^5*sqrt(-2*x + 1) - 3467/7
2*(2*x - 1)^4*sqrt(-2*x + 1) - 187/2*(2*x - 1)^3*sqrt(-2*x + 1) - 5929/80*(2*x -
1)^2*sqrt(-2*x + 1)