3.1856 \(\int (1-2 x)^{3/2} (2+3 x) (3+5 x)^2 \, dx\)

Optimal. Leaf size=53 \[ \frac{75}{88} (1-2 x)^{11/2}-\frac{505}{72} (1-2 x)^{9/2}+\frac{1133}{56} (1-2 x)^{7/2}-\frac{847}{40} (1-2 x)^{5/2} \]

[Out]

(-847*(1 - 2*x)^(5/2))/40 + (1133*(1 - 2*x)^(7/2))/56 - (505*(1 - 2*x)^(9/2))/72
+ (75*(1 - 2*x)^(11/2))/88

_______________________________________________________________________________________

Rubi [A]  time = 0.0449807, 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 \[ \frac{75}{88} (1-2 x)^{11/2}-\frac{505}{72} (1-2 x)^{9/2}+\frac{1133}{56} (1-2 x)^{7/2}-\frac{847}{40} (1-2 x)^{5/2} \]

Antiderivative was successfully verified.

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

[Out]

(-847*(1 - 2*x)^(5/2))/40 + (1133*(1 - 2*x)^(7/2))/56 - (505*(1 - 2*x)^(9/2))/72
+ (75*(1 - 2*x)^(11/2))/88

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 7.24041, size = 46, normalized size = 0.87 \[ \frac{75 \left (- 2 x + 1\right )^{\frac{11}{2}}}{88} - \frac{505 \left (- 2 x + 1\right )^{\frac{9}{2}}}{72} + \frac{1133 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} - \frac{847 \left (- 2 x + 1\right )^{\frac{5}{2}}}{40} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

75*(-2*x + 1)**(11/2)/88 - 505*(-2*x + 1)**(9/2)/72 + 1133*(-2*x + 1)**(7/2)/56
- 847*(-2*x + 1)**(5/2)/40

_______________________________________________________________________________________

Mathematica [A]  time = 0.0355021, size = 28, normalized size = 0.53 \[ -\frac{(1-2 x)^{5/2} \left (23625 x^3+61775 x^2+60715 x+24617\right )}{3465} \]

Antiderivative was successfully verified.

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

[Out]

-((1 - 2*x)^(5/2)*(24617 + 60715*x + 61775*x^2 + 23625*x^3))/3465

_______________________________________________________________________________________

Maple [A]  time = 0.005, size = 25, normalized size = 0.5 \[ -{\frac{23625\,{x}^{3}+61775\,{x}^{2}+60715\,x+24617}{3465} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/3465*(23625*x^3+61775*x^2+60715*x+24617)*(1-2*x)^(5/2)

_______________________________________________________________________________________

Maxima [A]  time = 1.36039, size = 50, normalized size = 0.94 \[ \frac{75}{88} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{505}{72} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{1133}{56} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{847}{40} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

75/88*(-2*x + 1)^(11/2) - 505/72*(-2*x + 1)^(9/2) + 1133/56*(-2*x + 1)^(7/2) - 8
47/40*(-2*x + 1)^(5/2)

_______________________________________________________________________________________

Fricas [A]  time = 0.210006, size = 46, normalized size = 0.87 \[ -\frac{1}{3465} \,{\left (94500 \, x^{5} + 152600 \, x^{4} + 19385 \, x^{3} - 82617 \, x^{2} - 37753 \, x + 24617\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/3465*(94500*x^5 + 152600*x^4 + 19385*x^3 - 82617*x^2 - 37753*x + 24617)*sqrt(
-2*x + 1)

_______________________________________________________________________________________

Sympy [A]  time = 2.71756, size = 46, normalized size = 0.87 \[ \frac{75 \left (- 2 x + 1\right )^{\frac{11}{2}}}{88} - \frac{505 \left (- 2 x + 1\right )^{\frac{9}{2}}}{72} + \frac{1133 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} - \frac{847 \left (- 2 x + 1\right )^{\frac{5}{2}}}{40} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

75*(-2*x + 1)**(11/2)/88 - 505*(-2*x + 1)**(9/2)/72 + 1133*(-2*x + 1)**(7/2)/56
- 847*(-2*x + 1)**(5/2)/40

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.214384, size = 88, normalized size = 1.66 \[ -\frac{75}{88} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{505}{72} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{1133}{56} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{847}{40} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-75/88*(2*x - 1)^5*sqrt(-2*x + 1) - 505/72*(2*x - 1)^4*sqrt(-2*x + 1) - 1133/56*
(2*x - 1)^3*sqrt(-2*x + 1) - 847/40*(2*x - 1)^2*sqrt(-2*x + 1)