3.1926 \(\int (1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^2 \, dx\)

Optimal. Leaf size=79 \[ \frac{675}{544} (1-2 x)^{17/2}-\frac{513}{32} (1-2 x)^{15/2}+\frac{17541}{208} (1-2 x)^{13/2}-\frac{39977}{176} (1-2 x)^{11/2}+\frac{91091}{288} (1-2 x)^{9/2}-\frac{5929}{32} (1-2 x)^{7/2} \]

[Out]

(-5929*(1 - 2*x)^(7/2))/32 + (91091*(1 - 2*x)^(9/2))/288 - (39977*(1 - 2*x)^(11/
2))/176 + (17541*(1 - 2*x)^(13/2))/208 - (513*(1 - 2*x)^(15/2))/32 + (675*(1 - 2
*x)^(17/2))/544

_______________________________________________________________________________________

Rubi [A]  time = 0.0678521, 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 \[ \frac{675}{544} (1-2 x)^{17/2}-\frac{513}{32} (1-2 x)^{15/2}+\frac{17541}{208} (1-2 x)^{13/2}-\frac{39977}{176} (1-2 x)^{11/2}+\frac{91091}{288} (1-2 x)^{9/2}-\frac{5929}{32} (1-2 x)^{7/2} \]

Antiderivative was successfully verified.

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

[Out]

(-5929*(1 - 2*x)^(7/2))/32 + (91091*(1 - 2*x)^(9/2))/288 - (39977*(1 - 2*x)^(11/
2))/176 + (17541*(1 - 2*x)^(13/2))/208 - (513*(1 - 2*x)^(15/2))/32 + (675*(1 - 2
*x)^(17/2))/544

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 9.50438, size = 70, normalized size = 0.89 \[ \frac{675 \left (- 2 x + 1\right )^{\frac{17}{2}}}{544} - \frac{513 \left (- 2 x + 1\right )^{\frac{15}{2}}}{32} + \frac{17541 \left (- 2 x + 1\right )^{\frac{13}{2}}}{208} - \frac{39977 \left (- 2 x + 1\right )^{\frac{11}{2}}}{176} + \frac{91091 \left (- 2 x + 1\right )^{\frac{9}{2}}}{288} - \frac{5929 \left (- 2 x + 1\right )^{\frac{7}{2}}}{32} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675*(-2*x + 1)**(17/2)/544 - 513*(-2*x + 1)**(15/2)/32 + 17541*(-2*x + 1)**(13/2
)/208 - 39977*(-2*x + 1)**(11/2)/176 + 91091*(-2*x + 1)**(9/2)/288 - 5929*(-2*x
+ 1)**(7/2)/32

_______________________________________________________________________________________

Mathematica [A]  time = 0.0554895, size = 38, normalized size = 0.48 \[ -\frac{(1-2 x)^{7/2} \left (868725 x^5+3440151 x^4+5708637 x^3+5069475 x^2+2497634 x+581846\right )}{21879} \]

Antiderivative was successfully verified.

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

[Out]

-((1 - 2*x)^(7/2)*(581846 + 2497634*x + 5069475*x^2 + 5708637*x^3 + 3440151*x^4
+ 868725*x^5))/21879

_______________________________________________________________________________________

Maple [A]  time = 0.007, size = 35, normalized size = 0.4 \[ -{\frac{868725\,{x}^{5}+3440151\,{x}^{4}+5708637\,{x}^{3}+5069475\,{x}^{2}+2497634\,x+581846}{21879} \left ( 1-2\,x \right ) ^{{\frac{7}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/21879*(868725*x^5+3440151*x^4+5708637*x^3+5069475*x^2+2497634*x+581846)*(1-2*
x)^(7/2)

_______________________________________________________________________________________

Maxima [A]  time = 1.35017, size = 74, normalized size = 0.94 \[ \frac{675}{544} \,{\left (-2 \, x + 1\right )}^{\frac{17}{2}} - \frac{513}{32} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{17541}{208} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{39977}{176} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{91091}{288} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{5929}{32} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675/544*(-2*x + 1)^(17/2) - 513/32*(-2*x + 1)^(15/2) + 17541/208*(-2*x + 1)^(13/
2) - 39977/176*(-2*x + 1)^(11/2) + 91091/288*(-2*x + 1)^(9/2) - 5929/32*(-2*x +
1)^(7/2)

_______________________________________________________________________________________

Fricas [A]  time = 0.231932, size = 66, normalized size = 0.84 \[ \frac{1}{21879} \,{\left (6949800 \, x^{8} + 17096508 \, x^{7} + 9599634 \, x^{6} - 8175663 \, x^{5} - 10040957 \, x^{4} - 608627 \, x^{3} + 2934177 \, x^{2} + 993442 \, x - 581846\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/21879*(6949800*x^8 + 17096508*x^7 + 9599634*x^6 - 8175663*x^5 - 10040957*x^4 -
608627*x^3 + 2934177*x^2 + 993442*x - 581846)*sqrt(-2*x + 1)

_______________________________________________________________________________________

Sympy [A]  time = 4.95616, size = 70, normalized size = 0.89 \[ \frac{675 \left (- 2 x + 1\right )^{\frac{17}{2}}}{544} - \frac{513 \left (- 2 x + 1\right )^{\frac{15}{2}}}{32} + \frac{17541 \left (- 2 x + 1\right )^{\frac{13}{2}}}{208} - \frac{39977 \left (- 2 x + 1\right )^{\frac{11}{2}}}{176} + \frac{91091 \left (- 2 x + 1\right )^{\frac{9}{2}}}{288} - \frac{5929 \left (- 2 x + 1\right )^{\frac{7}{2}}}{32} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675*(-2*x + 1)**(17/2)/544 - 513*(-2*x + 1)**(15/2)/32 + 17541*(-2*x + 1)**(13/2
)/208 - 39977*(-2*x + 1)**(11/2)/176 + 91091*(-2*x + 1)**(9/2)/288 - 5929*(-2*x
+ 1)**(7/2)/32

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.219473, size = 131, normalized size = 1.66 \[ \frac{675}{544} \,{\left (2 \, x - 1\right )}^{8} \sqrt{-2 \, x + 1} + \frac{513}{32} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} + \frac{17541}{208} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{39977}{176} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{91091}{288} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{5929}{32} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675/544*(2*x - 1)^8*sqrt(-2*x + 1) + 513/32*(2*x - 1)^7*sqrt(-2*x + 1) + 17541/2
08*(2*x - 1)^6*sqrt(-2*x + 1) + 39977/176*(2*x - 1)^5*sqrt(-2*x + 1) + 91091/288
*(2*x - 1)^4*sqrt(-2*x + 1) + 5929/32*(2*x - 1)^3*sqrt(-2*x + 1)