3.1913 \(\int (1-2 x)^{5/2} (2+3 x)^4 (3+5 x) \, dx\)

Optimal. Leaf size=79 \[ \frac{405}{544} (1-2 x)^{17/2}-\frac{1557}{160} (1-2 x)^{15/2}+\frac{10773}{208} (1-2 x)^{13/2}-\frac{24843}{176} (1-2 x)^{11/2}+\frac{57281}{288} (1-2 x)^{9/2}-\frac{3773}{32} (1-2 x)^{7/2} \]

[Out]

(-3773*(1 - 2*x)^(7/2))/32 + (57281*(1 - 2*x)^(9/2))/288 - (24843*(1 - 2*x)^(11/
2))/176 + (10773*(1 - 2*x)^(13/2))/208 - (1557*(1 - 2*x)^(15/2))/160 + (405*(1 -
2*x)^(17/2))/544

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Rubi [A]  time = 0.0635393, antiderivative size = 79, 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 \[ \frac{405}{544} (1-2 x)^{17/2}-\frac{1557}{160} (1-2 x)^{15/2}+\frac{10773}{208} (1-2 x)^{13/2}-\frac{24843}{176} (1-2 x)^{11/2}+\frac{57281}{288} (1-2 x)^{9/2}-\frac{3773}{32} (1-2 x)^{7/2} \]

Antiderivative was successfully verified.

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

[Out]

(-3773*(1 - 2*x)^(7/2))/32 + (57281*(1 - 2*x)^(9/2))/288 - (24843*(1 - 2*x)^(11/
2))/176 + (10773*(1 - 2*x)^(13/2))/208 - (1557*(1 - 2*x)^(15/2))/160 + (405*(1 -
2*x)^(17/2))/544

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Rubi in Sympy [A]  time = 9.01517, size = 70, normalized size = 0.89 \[ \frac{405 \left (- 2 x + 1\right )^{\frac{17}{2}}}{544} - \frac{1557 \left (- 2 x + 1\right )^{\frac{15}{2}}}{160} + \frac{10773 \left (- 2 x + 1\right )^{\frac{13}{2}}}{208} - \frac{24843 \left (- 2 x + 1\right )^{\frac{11}{2}}}{176} + \frac{57281 \left (- 2 x + 1\right )^{\frac{9}{2}}}{288} - \frac{3773 \left (- 2 x + 1\right )^{\frac{7}{2}}}{32} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

405*(-2*x + 1)**(17/2)/544 - 1557*(-2*x + 1)**(15/2)/160 + 10773*(-2*x + 1)**(13
/2)/208 - 24843*(-2*x + 1)**(11/2)/176 + 57281*(-2*x + 1)**(9/2)/288 - 3773*(-2*
x + 1)**(7/2)/32

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Mathematica [A]  time = 0.031797, size = 38, normalized size = 0.48 \[ -\frac{(1-2 x)^{7/2} \left (2606175 x^5+10517364 x^4+17777232 x^3+16066296 x^2+8043328 x+1899184\right )}{109395} \]

Antiderivative was successfully verified.

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

[Out]

-((1 - 2*x)^(7/2)*(1899184 + 8043328*x + 16066296*x^2 + 17777232*x^3 + 10517364*
x^4 + 2606175*x^5))/109395

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Maple [A]  time = 0.004, size = 35, normalized size = 0.4 \[ -{\frac{2606175\,{x}^{5}[phone]\,{x}^{4}[phone]\,{x}^{3}[phone]\,{x}^{2}+8043328\,x+1899184}{109395} \left ( 1-2\,x \right ) ^{{\frac{7}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/109395*(2606175*x^5+10517364*x^4+17777232*x^3+16066296*x^2+8043328*x+1899184)
*(1-2*x)^(7/2)

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Maxima [A]  time = 1.34435, size = 74, normalized size = 0.94 \[ \frac{405}{544} \,{\left (-2 \, x + 1\right )}^{\frac{17}{2}} - \frac{1557}{160} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{10773}{208} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{24843}{176} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{57281}{288} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{3773}{32} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

405/544*(-2*x + 1)^(17/2) - 1557/160*(-2*x + 1)^(15/2) + 10773/208*(-2*x + 1)^(1
3/2) - 24843/176*(-2*x + 1)^(11/2) + 57281/288*(-2*x + 1)^(9/2) - 3773/32*(-2*x
+ 1)^(7/2)

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Fricas [A]  time = 0.211099, size = 66, normalized size = 0.84 \[ \frac{1}{109395} \,{\left (20849400 \, x^{8} + 52864812 \, x^{7} + 31646538 \, x^{6} - 24298407 \, x^{5} - 32302900 \, x^{4} - 2705920 \, x^{3} + 9403464 \, x^{2} + 3351776 \, x - 1899184\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/109395*(20849400*x^8 + 52864812*x^7 + 31646538*x^6 - 24298407*x^5 - 32302900*x
^4 - 2705920*x^3 + 9403464*x^2 + 3351776*x - 1899184)*sqrt(-2*x + 1)

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Sympy [A]  time = 5.04977, size = 70, normalized size = 0.89 \[ \frac{405 \left (- 2 x + 1\right )^{\frac{17}{2}}}{544} - \frac{1557 \left (- 2 x + 1\right )^{\frac{15}{2}}}{160} + \frac{10773 \left (- 2 x + 1\right )^{\frac{13}{2}}}{208} - \frac{24843 \left (- 2 x + 1\right )^{\frac{11}{2}}}{176} + \frac{57281 \left (- 2 x + 1\right )^{\frac{9}{2}}}{288} - \frac{3773 \left (- 2 x + 1\right )^{\frac{7}{2}}}{32} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

405*(-2*x + 1)**(17/2)/544 - 1557*(-2*x + 1)**(15/2)/160 + 10773*(-2*x + 1)**(13
/2)/208 - 24843*(-2*x + 1)**(11/2)/176 + 57281*(-2*x + 1)**(9/2)/288 - 3773*(-2*
x + 1)**(7/2)/32

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GIAC/XCAS [A]  time = 0.213032, size = 131, normalized size = 1.66 \[ \frac{405}{544} \,{\left (2 \, x - 1\right )}^{8} \sqrt{-2 \, x + 1} + \frac{1557}{160} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} + \frac{10773}{208} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{24843}{176} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{57281}{288} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{3773}{32} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

405/544*(2*x - 1)^8*sqrt(-2*x + 1) + 1557/160*(2*x - 1)^7*sqrt(-2*x + 1) + 10773
/208*(2*x - 1)^6*sqrt(-2*x + 1) + 24843/176*(2*x - 1)^5*sqrt(-2*x + 1) + 57281/2
88*(2*x - 1)^4*sqrt(-2*x + 1) + 3773/32*(2*x - 1)^3*sqrt(-2*x + 1)