3.1996 \(\int \frac{(2+3 x)^4 (3+5 x)^2}{\sqrt{1-2 x}} \, dx\)

Optimal. Leaf size=92 \[ -\frac{2025}{832} (1-2 x)^{13/2}+\frac{13905}{352} (1-2 x)^{11/2}-\frac{17679}{64} (1-2 x)^{9/2}+\frac{17337}{16} (1-2 x)^{7/2}-\frac{832951}{320} (1-2 x)^{5/2}+\frac{381073}{96} (1-2 x)^{3/2}-\frac{290521}{64} \sqrt{1-2 x} \]

[Out]

(-290521*Sqrt[1 - 2*x])/64 + (381073*(1 - 2*x)^(3/2))/96 - (832951*(1 - 2*x)^(5/
2))/320 + (17337*(1 - 2*x)^(7/2))/16 - (17679*(1 - 2*x)^(9/2))/64 + (13905*(1 -
2*x)^(11/2))/352 - (2025*(1 - 2*x)^(13/2))/832

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Rubi [A]  time = 0.0769236, 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 \[ -\frac{2025}{832} (1-2 x)^{13/2}+\frac{13905}{352} (1-2 x)^{11/2}-\frac{17679}{64} (1-2 x)^{9/2}+\frac{17337}{16} (1-2 x)^{7/2}-\frac{832951}{320} (1-2 x)^{5/2}+\frac{381073}{96} (1-2 x)^{3/2}-\frac{290521}{64} \sqrt{1-2 x} \]

Antiderivative was successfully verified.

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

[Out]

(-290521*Sqrt[1 - 2*x])/64 + (381073*(1 - 2*x)^(3/2))/96 - (832951*(1 - 2*x)^(5/
2))/320 + (17337*(1 - 2*x)^(7/2))/16 - (17679*(1 - 2*x)^(9/2))/64 + (13905*(1 -
2*x)^(11/2))/352 - (2025*(1 - 2*x)^(13/2))/832

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Rubi in Sympy [A]  time = 10.2182, size = 82, normalized size = 0.89 \[ - \frac{2025 \left (- 2 x + 1\right )^{\frac{13}{2}}}{832} + \frac{13905 \left (- 2 x + 1\right )^{\frac{11}{2}}}{352} - \frac{17679 \left (- 2 x + 1\right )^{\frac{9}{2}}}{64} + \frac{17337 \left (- 2 x + 1\right )^{\frac{7}{2}}}{16} - \frac{832951 \left (- 2 x + 1\right )^{\frac{5}{2}}}{320} + \frac{381073 \left (- 2 x + 1\right )^{\frac{3}{2}}}{96} - \frac{290521 \sqrt{- 2 x + 1}}{64} \]

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]

-2025*(-2*x + 1)**(13/2)/832 + 13905*(-2*x + 1)**(11/2)/352 - 17679*(-2*x + 1)**
(9/2)/64 + 17337*(-2*x + 1)**(7/2)/16 - 832951*(-2*x + 1)**(5/2)/320 + 381073*(-
2*x + 1)**(3/2)/96 - 290521*sqrt(-2*x + 1)/64

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Mathematica [A]  time = 0.0528762, size = 43, normalized size = 0.47 \[ -\frac{\sqrt{1-2 x} \left (334125 x^6+1709100 x^5+3954645 x^4+5576580 x^3+5587044 x^2+4685656 x+4994536\right )}{2145} \]

Antiderivative was successfully verified.

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

[Out]

-(Sqrt[1 - 2*x]*(4994536 + 4685656*x + 5587044*x^2 + 5576580*x^3 + 3954645*x^4 +
1709100*x^5 + 334125*x^6))/2145

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Maple [A]  time = 0.007, size = 40, normalized size = 0.4 \[ -{\frac{334125\,{x}^{6}+1709100\,{x}^{5}+3954645\,{x}^{4}+5576580\,{x}^{3}+5587044\,{x}^{2}+4685656\,x+4994536}{2145}\sqrt{1-2\,x}} \]

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*(334125*x^6+1709100*x^5+3954645*x^4+5576580*x^3+5587044*x^2+4685656*x+49
94536)*(1-2*x)^(1/2)

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Maxima [A]  time = 1.35869, size = 86, normalized size = 0.93 \[ -\frac{2025}{832} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} + \frac{13905}{352} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{17679}{64} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{17337}{16} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{832951}{320} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{381073}{96} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{290521}{64} \, \sqrt{-2 \, x + 1} \]

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="maxima")

[Out]

-2025/832*(-2*x + 1)^(13/2) + 13905/352*(-2*x + 1)^(11/2) - 17679/64*(-2*x + 1)^
(9/2) + 17337/16*(-2*x + 1)^(7/2) - 832951/320*(-2*x + 1)^(5/2) + 381073/96*(-2*
x + 1)^(3/2) - 290521/64*sqrt(-2*x + 1)

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Fricas [A]  time = 0.214528, size = 53, normalized size = 0.58 \[ -\frac{1}{2145} \,{\left (334125 \, x^{6} + 1709100 \, x^{5} + 3954645 \, x^{4} + 5576580 \, x^{3} + 5587044 \, x^{2} + 4685656 \, x + 4994536\right )} \sqrt{-2 \, x + 1} \]

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*(334125*x^6 + 1709100*x^5 + 3954645*x^4 + 5576580*x^3 + 5587044*x^2 + 46
85656*x + 4994536)*sqrt(-2*x + 1)

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Sympy [A]  time = 18.7463, size = 82, normalized size = 0.89 \[ - \frac{2025 \left (- 2 x + 1\right )^{\frac{13}{2}}}{832} + \frac{13905 \left (- 2 x + 1\right )^{\frac{11}{2}}}{352} - \frac{17679 \left (- 2 x + 1\right )^{\frac{9}{2}}}{64} + \frac{17337 \left (- 2 x + 1\right )^{\frac{7}{2}}}{16} - \frac{832951 \left (- 2 x + 1\right )^{\frac{5}{2}}}{320} + \frac{381073 \left (- 2 x + 1\right )^{\frac{3}{2}}}{96} - \frac{290521 \sqrt{- 2 x + 1}}{64} \]

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]

-2025*(-2*x + 1)**(13/2)/832 + 13905*(-2*x + 1)**(11/2)/352 - 17679*(-2*x + 1)**
(9/2)/64 + 17337*(-2*x + 1)**(7/2)/16 - 832951*(-2*x + 1)**(5/2)/320 + 381073*(-
2*x + 1)**(3/2)/96 - 290521*sqrt(-2*x + 1)/64

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GIAC/XCAS [A]  time = 0.21014, size = 134, normalized size = 1.46 \[ -\frac{2025}{832} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} - \frac{13905}{352} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{17679}{64} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{17337}{16} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{832951}{320} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{381073}{96} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{290521}{64} \, \sqrt{-2 \, x + 1} \]

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="giac")

[Out]

-2025/832*(2*x - 1)^6*sqrt(-2*x + 1) - 13905/352*(2*x - 1)^5*sqrt(-2*x + 1) - 17
679/64*(2*x - 1)^4*sqrt(-2*x + 1) - 17337/16*(2*x - 1)^3*sqrt(-2*x + 1) - 832951
/320*(2*x - 1)^2*sqrt(-2*x + 1) + 381073/96*(-2*x + 1)^(3/2) - 290521/64*sqrt(-2
*x + 1)