3.1986 \(\int \frac{(2+3 x)^3 (3+5 x)}{\sqrt{1-2 x}} \, dx\)

Optimal. Leaf size=66 \[ -\frac{15}{16} (1-2 x)^{9/2}+\frac{621}{56} (1-2 x)^{7/2}-\frac{1071}{20} (1-2 x)^{5/2}+\frac{3283}{24} (1-2 x)^{3/2}-\frac{3773}{16} \sqrt{1-2 x} \]

[Out]

(-3773*Sqrt[1 - 2*x])/16 + (3283*(1 - 2*x)^(3/2))/24 - (1071*(1 - 2*x)^(5/2))/20
 + (621*(1 - 2*x)^(7/2))/56 - (15*(1 - 2*x)^(9/2))/16

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Rubi [A]  time = 0.0549475, antiderivative size = 66, 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 \[ -\frac{15}{16} (1-2 x)^{9/2}+\frac{621}{56} (1-2 x)^{7/2}-\frac{1071}{20} (1-2 x)^{5/2}+\frac{3283}{24} (1-2 x)^{3/2}-\frac{3773}{16} \sqrt{1-2 x} \]

Antiderivative was successfully verified.

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

[Out]

(-3773*Sqrt[1 - 2*x])/16 + (3283*(1 - 2*x)^(3/2))/24 - (1071*(1 - 2*x)^(5/2))/20
 + (621*(1 - 2*x)^(7/2))/56 - (15*(1 - 2*x)^(9/2))/16

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Rubi in Sympy [A]  time = 7.85605, size = 58, normalized size = 0.88 \[ - \frac{15 \left (- 2 x + 1\right )^{\frac{9}{2}}}{16} + \frac{621 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} - \frac{1071 \left (- 2 x + 1\right )^{\frac{5}{2}}}{20} + \frac{3283 \left (- 2 x + 1\right )^{\frac{3}{2}}}{24} - \frac{3773 \sqrt{- 2 x + 1}}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15*(-2*x + 1)**(9/2)/16 + 621*(-2*x + 1)**(7/2)/56 - 1071*(-2*x + 1)**(5/2)/20
+ 3283*(-2*x + 1)**(3/2)/24 - 3773*sqrt(-2*x + 1)/16

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Mathematica [A]  time = 0.03255, size = 33, normalized size = 0.5 \[ -\frac{1}{105} \sqrt{1-2 x} \left (1575 x^4+6165 x^3+10881 x^2+12434 x+14954\right ) \]

Antiderivative was successfully verified.

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

[Out]

-(Sqrt[1 - 2*x]*(14954 + 12434*x + 10881*x^2 + 6165*x^3 + 1575*x^4))/105

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Maple [A]  time = 0.005, size = 30, normalized size = 0.5 \[ -{\frac{1575\,{x}^{4}+6165\,{x}^{3}+10881\,{x}^{2}+12434\,x+14954}{105}\sqrt{1-2\,x}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/105*(1575*x^4+6165*x^3+10881*x^2+12434*x+14954)*(1-2*x)^(1/2)

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Maxima [A]  time = 1.34887, size = 62, normalized size = 0.94 \[ -\frac{15}{16} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{621}{56} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{1071}{20} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{3283}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{3773}{16} \, \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15/16*(-2*x + 1)^(9/2) + 621/56*(-2*x + 1)^(7/2) - 1071/20*(-2*x + 1)^(5/2) + 3
283/24*(-2*x + 1)^(3/2) - 3773/16*sqrt(-2*x + 1)

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Fricas [A]  time = 0.209404, size = 39, normalized size = 0.59 \[ -\frac{1}{105} \,{\left (1575 \, x^{4} + 6165 \, x^{3} + 10881 \, x^{2} + 12434 \, x + 14954\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/105*(1575*x^4 + 6165*x^3 + 10881*x^2 + 12434*x + 14954)*sqrt(-2*x + 1)

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Sympy [A]  time = 9.9098, size = 58, normalized size = 0.88 \[ - \frac{15 \left (- 2 x + 1\right )^{\frac{9}{2}}}{16} + \frac{621 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} - \frac{1071 \left (- 2 x + 1\right )^{\frac{5}{2}}}{20} + \frac{3283 \left (- 2 x + 1\right )^{\frac{3}{2}}}{24} - \frac{3773 \sqrt{- 2 x + 1}}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15*(-2*x + 1)**(9/2)/16 + 621*(-2*x + 1)**(7/2)/56 - 1071*(-2*x + 1)**(5/2)/20
+ 3283*(-2*x + 1)**(3/2)/24 - 3773*sqrt(-2*x + 1)/16

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GIAC/XCAS [A]  time = 0.20752, size = 90, normalized size = 1.36 \[ -\frac{15}{16} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{621}{56} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{1071}{20} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{3283}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{3773}{16} \, \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15/16*(2*x - 1)^4*sqrt(-2*x + 1) - 621/56*(2*x - 1)^3*sqrt(-2*x + 1) - 1071/20*
(2*x - 1)^2*sqrt(-2*x + 1) + 3283/24*(-2*x + 1)^(3/2) - 3773/16*sqrt(-2*x + 1)