3.1844 \(\int (1-2 x)^{3/2} (2+3 x)^2 (3+5 x) \, dx\)

Optimal. Leaf size=53 \[ \frac{45}{88} (1-2 x)^{11/2}-\frac{103}{24} (1-2 x)^{9/2}+\frac{101}{8} (1-2 x)^{7/2}-\frac{539}{40} (1-2 x)^{5/2} \]

[Out]

(-539*(1 - 2*x)^(5/2))/40 + (101*(1 - 2*x)^(7/2))/8 - (103*(1 - 2*x)^(9/2))/24 +
(45*(1 - 2*x)^(11/2))/88

_______________________________________________________________________________________

Rubi [A]  time = 0.0467812, antiderivative size = 53, 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 \[ \frac{45}{88} (1-2 x)^{11/2}-\frac{103}{24} (1-2 x)^{9/2}+\frac{101}{8} (1-2 x)^{7/2}-\frac{539}{40} (1-2 x)^{5/2} \]

Antiderivative was successfully verified.

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

[Out]

(-539*(1 - 2*x)^(5/2))/40 + (101*(1 - 2*x)^(7/2))/8 - (103*(1 - 2*x)^(9/2))/24 +
(45*(1 - 2*x)^(11/2))/88

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 7.21313, size = 46, normalized size = 0.87 \[ \frac{45 \left (- 2 x + 1\right )^{\frac{11}{2}}}{88} - \frac{103 \left (- 2 x + 1\right )^{\frac{9}{2}}}{24} + \frac{101 \left (- 2 x + 1\right )^{\frac{7}{2}}}{8} - \frac{539 \left (- 2 x + 1\right )^{\frac{5}{2}}}{40} \]

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),x)

[Out]

45*(-2*x + 1)**(11/2)/88 - 103*(-2*x + 1)**(9/2)/24 + 101*(-2*x + 1)**(7/2)/8 -
539*(-2*x + 1)**(5/2)/40

_______________________________________________________________________________________

Mathematica [A]  time = 0.0368172, size = 28, normalized size = 0.53 \[ -\frac{1}{165} (1-2 x)^{5/2} \left (675 x^3+1820 x^2+1840 x+764\right ) \]

Antiderivative was successfully verified.

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

[Out]

-((1 - 2*x)^(5/2)*(764 + 1840*x + 1820*x^2 + 675*x^3))/165

_______________________________________________________________________________________

Maple [A]  time = 0.005, size = 25, normalized size = 0.5 \[ -{\frac{675\,{x}^{3}+1820\,{x}^{2}+1840\,x+764}{165} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/165*(675*x^3+1820*x^2+1840*x+764)*(1-2*x)^(5/2)

_______________________________________________________________________________________

Maxima [A]  time = 1.34336, size = 50, normalized size = 0.94 \[ \frac{45}{88} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{103}{24} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{101}{8} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{539}{40} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

45/88*(-2*x + 1)^(11/2) - 103/24*(-2*x + 1)^(9/2) + 101/8*(-2*x + 1)^(7/2) - 539
/40*(-2*x + 1)^(5/2)

_______________________________________________________________________________________

Fricas [A]  time = 0.219789, size = 46, normalized size = 0.87 \[ -\frac{1}{165} \,{\left (2700 \, x^{5} + 4580 \, x^{4} + 755 \, x^{3} - 2484 \, x^{2} - 1216 \, x + 764\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/165*(2700*x^5 + 4580*x^4 + 755*x^3 - 2484*x^2 - 1216*x + 764)*sqrt(-2*x + 1)

_______________________________________________________________________________________

Sympy [A]  time = 5.64208, size = 46, normalized size = 0.87 \[ \frac{45 \left (- 2 x + 1\right )^{\frac{11}{2}}}{88} - \frac{103 \left (- 2 x + 1\right )^{\frac{9}{2}}}{24} + \frac{101 \left (- 2 x + 1\right )^{\frac{7}{2}}}{8} - \frac{539 \left (- 2 x + 1\right )^{\frac{5}{2}}}{40} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

45*(-2*x + 1)**(11/2)/88 - 103*(-2*x + 1)**(9/2)/24 + 101*(-2*x + 1)**(7/2)/8 -
539*(-2*x + 1)**(5/2)/40

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.227437, size = 88, normalized size = 1.66 \[ -\frac{45}{88} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{103}{24} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{101}{8} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{539}{40} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-45/88*(2*x - 1)^5*sqrt(-2*x + 1) - 103/24*(2*x - 1)^4*sqrt(-2*x + 1) - 101/8*(2
*x - 1)^3*sqrt(-2*x + 1) - 539/40*(2*x - 1)^2*sqrt(-2*x + 1)