3.1987 \(\int \frac{(2+3 x)^2 (3+5 x)}{\sqrt{1-2 x}} \, dx\)

Optimal. Leaf size=53 \[ \frac{45}{56} (1-2 x)^{7/2}-\frac{309}{40} (1-2 x)^{5/2}+\frac{707}{24} (1-2 x)^{3/2}-\frac{539}{8} \sqrt{1-2 x} \]

[Out]

(-539*Sqrt[1 - 2*x])/8 + (707*(1 - 2*x)^(3/2))/24 - (309*(1 - 2*x)^(5/2))/40 + (
45*(1 - 2*x)^(7/2))/56

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Rubi [A]  time = 0.0521432, 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 \[ \frac{45}{56} (1-2 x)^{7/2}-\frac{309}{40} (1-2 x)^{5/2}+\frac{707}{24} (1-2 x)^{3/2}-\frac{539}{8} \sqrt{1-2 x} \]

Antiderivative was successfully verified.

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

[Out]

(-539*Sqrt[1 - 2*x])/8 + (707*(1 - 2*x)^(3/2))/24 - (309*(1 - 2*x)^(5/2))/40 + (
45*(1 - 2*x)^(7/2))/56

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Rubi in Sympy [A]  time = 6.90542, size = 46, normalized size = 0.87 \[ \frac{45 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} - \frac{309 \left (- 2 x + 1\right )^{\frac{5}{2}}}{40} + \frac{707 \left (- 2 x + 1\right )^{\frac{3}{2}}}{24} - \frac{539 \sqrt{- 2 x + 1}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

45*(-2*x + 1)**(7/2)/56 - 309*(-2*x + 1)**(5/2)/40 + 707*(-2*x + 1)**(3/2)/24 -
539*sqrt(-2*x + 1)/8

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Mathematica [A]  time = 0.0302858, size = 28, normalized size = 0.53 \[ -\frac{1}{105} \sqrt{1-2 x} \left (675 x^3+2232 x^2+3448 x+4708\right ) \]

Antiderivative was successfully verified.

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

[Out]

-(Sqrt[1 - 2*x]*(4708 + 3448*x + 2232*x^2 + 675*x^3))/105

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Maple [A]  time = 0.004, size = 25, normalized size = 0.5 \[ -{\frac{675\,{x}^{3}+2232\,{x}^{2}+3448\,x+4708}{105}\sqrt{1-2\,x}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/105*(675*x^3+2232*x^2+3448*x+4708)*(1-2*x)^(1/2)

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Maxima [A]  time = 1.35547, size = 50, normalized size = 0.94 \[ \frac{45}{56} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{309}{40} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{707}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{539}{8} \, \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

45/56*(-2*x + 1)^(7/2) - 309/40*(-2*x + 1)^(5/2) + 707/24*(-2*x + 1)^(3/2) - 539
/8*sqrt(-2*x + 1)

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Fricas [A]  time = 0.225527, size = 32, normalized size = 0.6 \[ -\frac{1}{105} \,{\left (675 \, x^{3} + 2232 \, x^{2} + 3448 \, x + 4708\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/105*(675*x^3 + 2232*x^2 + 3448*x + 4708)*sqrt(-2*x + 1)

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Sympy [A]  time = 6.63422, size = 46, normalized size = 0.87 \[ \frac{45 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} - \frac{309 \left (- 2 x + 1\right )^{\frac{5}{2}}}{40} + \frac{707 \left (- 2 x + 1\right )^{\frac{3}{2}}}{24} - \frac{539 \sqrt{- 2 x + 1}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

45*(-2*x + 1)**(7/2)/56 - 309*(-2*x + 1)**(5/2)/40 + 707*(-2*x + 1)**(3/2)/24 -
539*sqrt(-2*x + 1)/8

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GIAC/XCAS [A]  time = 0.20726, size = 69, normalized size = 1.3 \[ -\frac{45}{56} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{309}{40} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{707}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{539}{8} \, \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-45/56*(2*x - 1)^3*sqrt(-2*x + 1) - 309/40*(2*x - 1)^2*sqrt(-2*x + 1) + 707/24*(
-2*x + 1)^(3/2) - 539/8*sqrt(-2*x + 1)