3.1786 \(\int \sqrt{1-2 x} (2+3 x)^4 (3+5 x)^2 \, dx\)

Optimal. Leaf size=92 \[ -\frac{135}{64} (1-2 x)^{15/2}+\frac{13905}{416} (1-2 x)^{13/2}-\frac{159111}{704} (1-2 x)^{11/2}+\frac{40453}{48} (1-2 x)^{9/2}-\frac{118993}{64} (1-2 x)^{7/2}+\frac{381073}{160} (1-2 x)^{5/2}-\frac{290521}{192} (1-2 x)^{3/2} \]

[Out]

(-290521*(1 - 2*x)^(3/2))/192 + (381073*(1 - 2*x)^(5/2))/160 - (118993*(1 - 2*x)
^(7/2))/64 + (40453*(1 - 2*x)^(9/2))/48 - (159111*(1 - 2*x)^(11/2))/704 + (13905
*(1 - 2*x)^(13/2))/416 - (135*(1 - 2*x)^(15/2))/64

_______________________________________________________________________________________

Rubi [A]  time = 0.0684216, antiderivative size = 92, 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 \[ -\frac{135}{64} (1-2 x)^{15/2}+\frac{13905}{416} (1-2 x)^{13/2}-\frac{159111}{704} (1-2 x)^{11/2}+\frac{40453}{48} (1-2 x)^{9/2}-\frac{118993}{64} (1-2 x)^{7/2}+\frac{381073}{160} (1-2 x)^{5/2}-\frac{290521}{192} (1-2 x)^{3/2} \]

Antiderivative was successfully verified.

[In]  Int[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^2,x]

[Out]

(-290521*(1 - 2*x)^(3/2))/192 + (381073*(1 - 2*x)^(5/2))/160 - (118993*(1 - 2*x)
^(7/2))/64 + (40453*(1 - 2*x)^(9/2))/48 - (159111*(1 - 2*x)^(11/2))/704 + (13905
*(1 - 2*x)^(13/2))/416 - (135*(1 - 2*x)^(15/2))/64

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 10.3154, size = 82, normalized size = 0.89 \[ - \frac{135 \left (- 2 x + 1\right )^{\frac{15}{2}}}{64} + \frac{13905 \left (- 2 x + 1\right )^{\frac{13}{2}}}{416} - \frac{159111 \left (- 2 x + 1\right )^{\frac{11}{2}}}{704} + \frac{40453 \left (- 2 x + 1\right )^{\frac{9}{2}}}{48} - \frac{118993 \left (- 2 x + 1\right )^{\frac{7}{2}}}{64} + \frac{381073 \left (- 2 x + 1\right )^{\frac{5}{2}}}{160} - \frac{290521 \left (- 2 x + 1\right )^{\frac{3}{2}}}{192} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**4*(3+5*x)**2*(1-2*x)**(1/2),x)

[Out]

-135*(-2*x + 1)**(15/2)/64 + 13905*(-2*x + 1)**(13/2)/416 - 159111*(-2*x + 1)**(
11/2)/704 + 40453*(-2*x + 1)**(9/2)/48 - 118993*(-2*x + 1)**(7/2)/64 + 381073*(-
2*x + 1)**(5/2)/160 - 290521*(-2*x + 1)**(3/2)/192

_______________________________________________________________________________________

Mathematica [A]  time = 0.0593655, size = 43, normalized size = 0.47 \[ -\frac{(1-2 x)^{3/2} \left (289575 x^6+1425600 x^5+3106755 x^4+3960500 x^3+3298140 x^2+1895832 x+734904\right )}{2145} \]

Antiderivative was successfully verified.

[In]  Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^2,x]

[Out]

-((1 - 2*x)^(3/2)*(734904 + 1895832*x + 3298140*x^2 + 3960500*x^3 + 3106755*x^4
+ 1425600*x^5 + 289575*x^6))/2145

_______________________________________________________________________________________

Maple [A]  time = 0.006, size = 40, normalized size = 0.4 \[ -{\frac{289575\,{x}^{6}+1425600\,{x}^{5}+3106755\,{x}^{4}+3960500\,{x}^{3}+3298140\,{x}^{2}+1895832\,x+734904}{2145} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^4*(3+5*x)^2*(1-2*x)^(1/2),x)

[Out]

-1/2145*(289575*x^6+1425600*x^5+3106755*x^4+3960500*x^3+3298140*x^2+1895832*x+73
4904)*(1-2*x)^(3/2)

_______________________________________________________________________________________

Maxima [A]  time = 1.34927, size = 86, normalized size = 0.93 \[ -\frac{135}{64} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{13905}{416} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{159111}{704} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{40453}{48} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{118993}{64} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{381073}{160} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{290521}{192} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^4*sqrt(-2*x + 1),x, algorithm="maxima")

[Out]

-135/64*(-2*x + 1)^(15/2) + 13905/416*(-2*x + 1)^(13/2) - 159111/704*(-2*x + 1)^
(11/2) + 40453/48*(-2*x + 1)^(9/2) - 118993/64*(-2*x + 1)^(7/2) + 381073/160*(-2
*x + 1)^(5/2) - 290521/192*(-2*x + 1)^(3/2)

_______________________________________________________________________________________

Fricas [A]  time = 0.206349, size = 59, normalized size = 0.64 \[ \frac{1}{2145} \,{\left (579150 \, x^{7} + 2561625 \, x^{6} + 4787910 \, x^{5} + 4814245 \, x^{4} + 2635780 \, x^{3} + 493524 \, x^{2} - 426024 \, x - 734904\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^4*sqrt(-2*x + 1),x, algorithm="fricas")

[Out]

1/2145*(579150*x^7 + 2561625*x^6 + 4787910*x^5 + 4814245*x^4 + 2635780*x^3 + 493
524*x^2 - 426024*x - 734904)*sqrt(-2*x + 1)

_______________________________________________________________________________________

Sympy [A]  time = 3.36127, size = 82, normalized size = 0.89 \[ - \frac{135 \left (- 2 x + 1\right )^{\frac{15}{2}}}{64} + \frac{13905 \left (- 2 x + 1\right )^{\frac{13}{2}}}{416} - \frac{159111 \left (- 2 x + 1\right )^{\frac{11}{2}}}{704} + \frac{40453 \left (- 2 x + 1\right )^{\frac{9}{2}}}{48} - \frac{118993 \left (- 2 x + 1\right )^{\frac{7}{2}}}{64} + \frac{381073 \left (- 2 x + 1\right )^{\frac{5}{2}}}{160} - \frac{290521 \left (- 2 x + 1\right )^{\frac{3}{2}}}{192} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**4*(3+5*x)**2*(1-2*x)**(1/2),x)

[Out]

-135*(-2*x + 1)**(15/2)/64 + 13905*(-2*x + 1)**(13/2)/416 - 159111*(-2*x + 1)**(
11/2)/704 + 40453*(-2*x + 1)**(9/2)/48 - 118993*(-2*x + 1)**(7/2)/64 + 381073*(-
2*x + 1)**(5/2)/160 - 290521*(-2*x + 1)**(3/2)/192

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.216021, size = 143, normalized size = 1.55 \[ \frac{135}{64} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} + \frac{13905}{416} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{159111}{704} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{40453}{48} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{118993}{64} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{381073}{160} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{290521}{192} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^4*sqrt(-2*x + 1),x, algorithm="giac")

[Out]

135/64*(2*x - 1)^7*sqrt(-2*x + 1) + 13905/416*(2*x - 1)^6*sqrt(-2*x + 1) + 15911
1/704*(2*x - 1)^5*sqrt(-2*x + 1) + 40453/48*(2*x - 1)^4*sqrt(-2*x + 1) + 118993/
64*(2*x - 1)^3*sqrt(-2*x + 1) + 381073/160*(2*x - 1)^2*sqrt(-2*x + 1) - 290521/1
92*(-2*x + 1)^(3/2)