3.1984 \(\int \frac{(2+3 x)^5 (3+5 x)}{\sqrt{1-2 x}} \, dx\)

Optimal. Leaf size=92 \[ -\frac{1215}{832} (1-2 x)^{13/2}+\frac{1053}{44} (1-2 x)^{11/2}-\frac{10815}{64} (1-2 x)^{9/2}+\frac{5355}{8} (1-2 x)^{7/2}-\frac{103929}{64} (1-2 x)^{5/2}+\frac{60025}{24} (1-2 x)^{3/2}-\frac{184877}{64} \sqrt{1-2 x} \]

[Out]

(-184877*Sqrt[1 - 2*x])/64 + (60025*(1 - 2*x)^(3/2))/24 - (103929*(1 - 2*x)^(5/2
))/64 + (5355*(1 - 2*x)^(7/2))/8 - (10815*(1 - 2*x)^(9/2))/64 + (1053*(1 - 2*x)^
(11/2))/44 - (1215*(1 - 2*x)^(13/2))/832

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Rubi [A]  time = 0.0677545, antiderivative size = 92, 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 \[ -\frac{1215}{832} (1-2 x)^{13/2}+\frac{1053}{44} (1-2 x)^{11/2}-\frac{10815}{64} (1-2 x)^{9/2}+\frac{5355}{8} (1-2 x)^{7/2}-\frac{103929}{64} (1-2 x)^{5/2}+\frac{60025}{24} (1-2 x)^{3/2}-\frac{184877}{64} \sqrt{1-2 x} \]

Antiderivative was successfully verified.

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

[Out]

(-184877*Sqrt[1 - 2*x])/64 + (60025*(1 - 2*x)^(3/2))/24 - (103929*(1 - 2*x)^(5/2
))/64 + (5355*(1 - 2*x)^(7/2))/8 - (10815*(1 - 2*x)^(9/2))/64 + (1053*(1 - 2*x)^
(11/2))/44 - (1215*(1 - 2*x)^(13/2))/832

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Rubi in Sympy [A]  time = 9.62075, size = 82, normalized size = 0.89 \[ - \frac{1215 \left (- 2 x + 1\right )^{\frac{13}{2}}}{832} + \frac{1053 \left (- 2 x + 1\right )^{\frac{11}{2}}}{44} - \frac{10815 \left (- 2 x + 1\right )^{\frac{9}{2}}}{64} + \frac{5355 \left (- 2 x + 1\right )^{\frac{7}{2}}}{8} - \frac{103929 \left (- 2 x + 1\right )^{\frac{5}{2}}}{64} + \frac{60025 \left (- 2 x + 1\right )^{\frac{3}{2}}}{24} - \frac{184877 \sqrt{- 2 x + 1}}{64} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1215*(-2*x + 1)**(13/2)/832 + 1053*(-2*x + 1)**(11/2)/44 - 10815*(-2*x + 1)**(9
/2)/64 + 5355*(-2*x + 1)**(7/2)/8 - 103929*(-2*x + 1)**(5/2)/64 + 60025*(-2*x +
1)**(3/2)/24 - 184877*sqrt(-2*x + 1)/64

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Mathematica [A]  time = 0.0397604, size = 43, normalized size = 0.47 \[ -\frac{1}{429} \sqrt{1-2 x} \left (40095 x^6+208251 x^5+488925 x^4+698580 x^3+707436 x^2+597464 x+638648\right ) \]

Antiderivative was successfully verified.

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

[Out]

-(Sqrt[1 - 2*x]*(638648 + 597464*x + 707436*x^2 + 698580*x^3 + 488925*x^4 + 2082
51*x^5 + 40095*x^6))/429

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Maple [A]  time = 0.008, size = 40, normalized size = 0.4 \[ -{\frac{40095\,{x}^{6}+208251\,{x}^{5}+488925\,{x}^{4}+698580\,{x}^{3}+707436\,{x}^{2}+597464\,x+638648}{429}\sqrt{1-2\,x}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/429*(40095*x^6+208251*x^5+488925*x^4+698580*x^3+707436*x^2+597464*x+638648)*(
1-2*x)^(1/2)

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Maxima [A]  time = 1.34737, size = 86, normalized size = 0.93 \[ -\frac{1215}{832} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} + \frac{1053}{44} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{10815}{64} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{5355}{8} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{103929}{64} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{60025}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{184877}{64} \, \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1215/832*(-2*x + 1)^(13/2) + 1053/44*(-2*x + 1)^(11/2) - 10815/64*(-2*x + 1)^(9
/2) + 5355/8*(-2*x + 1)^(7/2) - 103929/64*(-2*x + 1)^(5/2) + 60025/24*(-2*x + 1)
^(3/2) - 184877/64*sqrt(-2*x + 1)

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Fricas [A]  time = 0.208314, size = 53, normalized size = 0.58 \[ -\frac{1}{429} \,{\left (40095 \, x^{6} + 208251 \, x^{5} + 488925 \, x^{4} + 698580 \, x^{3} + 707436 \, x^{2} + 597464 \, x + 638648\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/429*(40095*x^6 + 208251*x^5 + 488925*x^4 + 698580*x^3 + 707436*x^2 + 597464*x
+ 638648)*sqrt(-2*x + 1)

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Sympy [A]  time = 18.8198, size = 82, normalized size = 0.89 \[ - \frac{1215 \left (- 2 x + 1\right )^{\frac{13}{2}}}{832} + \frac{1053 \left (- 2 x + 1\right )^{\frac{11}{2}}}{44} - \frac{10815 \left (- 2 x + 1\right )^{\frac{9}{2}}}{64} + \frac{5355 \left (- 2 x + 1\right )^{\frac{7}{2}}}{8} - \frac{103929 \left (- 2 x + 1\right )^{\frac{5}{2}}}{64} + \frac{60025 \left (- 2 x + 1\right )^{\frac{3}{2}}}{24} - \frac{184877 \sqrt{- 2 x + 1}}{64} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1215*(-2*x + 1)**(13/2)/832 + 1053*(-2*x + 1)**(11/2)/44 - 10815*(-2*x + 1)**(9
/2)/64 + 5355*(-2*x + 1)**(7/2)/8 - 103929*(-2*x + 1)**(5/2)/64 + 60025*(-2*x +
1)**(3/2)/24 - 184877*sqrt(-2*x + 1)/64

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GIAC/XCAS [A]  time = 0.209001, size = 134, normalized size = 1.46 \[ -\frac{1215}{832} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} - \frac{1053}{44} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{10815}{64} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{5355}{8} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{103929}{64} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{60025}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{184877}{64} \, \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1215/832*(2*x - 1)^6*sqrt(-2*x + 1) - 1053/44*(2*x - 1)^5*sqrt(-2*x + 1) - 1081
5/64*(2*x - 1)^4*sqrt(-2*x + 1) - 5355/8*(2*x - 1)^3*sqrt(-2*x + 1) - 103929/64*
(2*x - 1)^2*sqrt(-2*x + 1) + 60025/24*(-2*x + 1)^(3/2) - 184877/64*sqrt(-2*x + 1
)