3.1865 \(\int (1-2 x)^{3/2} (2+3 x)^4 (3+5 x)^3 \, dx\)

Optimal. Leaf size=105 \[ \frac{10125 (1-2 x)^{19/2}}{2432}-\frac{161325 (1-2 x)^{17/2}}{2176}+\frac{73431}{128} (1-2 x)^{15/2}-\frac{4177401 (1-2 x)^{13/2}}{1664}+\frac{9504551 (1-2 x)^{11/2}}{1408}-\frac{4324397}{384} (1-2 x)^{9/2}+\frac{1405173}{128} (1-2 x)^{7/2}-\frac{3195731}{640} (1-2 x)^{5/2} \]

[Out]

(-3195731*(1 - 2*x)^(5/2))/640 + (1405173*(1 - 2*x)^(7/2))/128 - (4324397*(1 - 2
*x)^(9/2))/384 + (9504551*(1 - 2*x)^(11/2))/1408 - (4177401*(1 - 2*x)^(13/2))/16
64 + (73431*(1 - 2*x)^(15/2))/128 - (161325*(1 - 2*x)^(17/2))/2176 + (10125*(1 -
2*x)^(19/2))/2432

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Rubi [A]  time = 0.0743113, antiderivative size = 105, 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 \[ \frac{10125 (1-2 x)^{19/2}}{2432}-\frac{161325 (1-2 x)^{17/2}}{2176}+\frac{73431}{128} (1-2 x)^{15/2}-\frac{4177401 (1-2 x)^{13/2}}{1664}+\frac{9504551 (1-2 x)^{11/2}}{1408}-\frac{4324397}{384} (1-2 x)^{9/2}+\frac{1405173}{128} (1-2 x)^{7/2}-\frac{3195731}{640} (1-2 x)^{5/2} \]

Antiderivative was successfully verified.

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

[Out]

(-3195731*(1 - 2*x)^(5/2))/640 + (1405173*(1 - 2*x)^(7/2))/128 - (4324397*(1 - 2
*x)^(9/2))/384 + (9504551*(1 - 2*x)^(11/2))/1408 - (4177401*(1 - 2*x)^(13/2))/16
64 + (73431*(1 - 2*x)^(15/2))/128 - (161325*(1 - 2*x)^(17/2))/2176 + (10125*(1 -
2*x)^(19/2))/2432

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Rubi in Sympy [A]  time = 12.1596, size = 94, normalized size = 0.9 \[ \frac{10125 \left (- 2 x + 1\right )^{\frac{19}{2}}}{2432} - \frac{161325 \left (- 2 x + 1\right )^{\frac{17}{2}}}{2176} + \frac{73431 \left (- 2 x + 1\right )^{\frac{15}{2}}}{128} - \frac{4177401 \left (- 2 x + 1\right )^{\frac{13}{2}}}{1664} + \frac{9504551 \left (- 2 x + 1\right )^{\frac{11}{2}}}{1408} - \frac{4324397 \left (- 2 x + 1\right )^{\frac{9}{2}}}{384} + \frac{1405173 \left (- 2 x + 1\right )^{\frac{7}{2}}}{128} - \frac{3195731 \left (- 2 x + 1\right )^{\frac{5}{2}}}{640} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

10125*(-2*x + 1)**(19/2)/2432 - 161325*(-2*x + 1)**(17/2)/2176 + 73431*(-2*x + 1
)**(15/2)/128 - 4177401*(-2*x + 1)**(13/2)/1664 + 9504551*(-2*x + 1)**(11/2)/140
8 - 4324397*(-2*x + 1)**(9/2)/384 + 1405173*(-2*x + 1)**(7/2)/128 - 3195731*(-2*
x + 1)**(5/2)/640

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Mathematica [A]  time = 0.0649255, size = 48, normalized size = 0.46 \[ -\frac{(1-2 x)^{5/2} \left (369208125 x^7+1995171750 x^6+4795033815 x^5+6744559140 x^4+6142984080 x^3+3771434840 x^2+1547888800 x+369438704\right )}{692835} \]

Antiderivative was successfully verified.

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

[Out]

-((1 - 2*x)^(5/2)*(369438704 + 1547888800*x + 3771434840*x^2 + 6142984080*x^3 +
6744559140*x^4 + 4795033815*x^5 + 1995171750*x^6 + 369208125*x^7))/692835

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Maple [A]  time = 0.006, size = 45, normalized size = 0.4 \[ -{\frac{369208125\,{x}^{7}[phone]\,{x}^{6}[phone]\,{x}^{5}[phone]\,{x}^{4}[phone]\,{x}^{3}[phone]\,{x}^{2}[phone]\,x+369438704}{692835} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/692835*(369208125*x^7+1995171750*x^6+4795033815*x^5+6744559140*x^4+6142984080
*x^3+3771434840*x^2+1547888800*x+369438704)*(1-2*x)^(5/2)

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Maxima [A]  time = 1.34966, size = 99, normalized size = 0.94 \[ \frac{10125}{2432} \,{\left (-2 \, x + 1\right )}^{\frac{19}{2}} - \frac{161325}{2176} \,{\left (-2 \, x + 1\right )}^{\frac{17}{2}} + \frac{73431}{128} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} - \frac{4177401}{1664} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} + \frac{9504551}{1408} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{4324397}{384} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{1405173}{128} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{3195731}{640} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

10125/2432*(-2*x + 1)^(19/2) - 161325/2176*(-2*x + 1)^(17/2) + 73431/128*(-2*x +
1)^(15/2) - 4177401/1664*(-2*x + 1)^(13/2) + 9504551/1408*(-2*x + 1)^(11/2) - 4
324397/384*(-2*x + 1)^(9/2) + 1405173/128*(-2*x + 1)^(7/2) - 3195731/640*(-2*x +
1)^(5/2)

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Fricas [A]  time = 0.206876, size = 73, normalized size = 0.7 \[ -\frac{1}{692835} \,{\left (1476832500 \, x^{9} + 6503854500 \, x^{8} + 11568656385 \, x^{7} + 9793273050 \, x^{6} + 2388733575 \, x^{5} - 2741637820 \, x^{4} - 2751200080 \, x^{3} - 942365544 \, x^{2} + 70133984 \, x + 369438704\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/692835*(1476832500*x^9 + 6503854500*x^8 + 11568656385*x^7 + 9793273050*x^6 +
2388733575*x^5 - 2741637820*x^4 - 2751200080*x^3 - 942365544*x^2 + 70133984*x +
369438704)*sqrt(-2*x + 1)

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Sympy [A]  time = 4.82992, size = 94, normalized size = 0.9 \[ \frac{10125 \left (- 2 x + 1\right )^{\frac{19}{2}}}{2432} - \frac{161325 \left (- 2 x + 1\right )^{\frac{17}{2}}}{2176} + \frac{73431 \left (- 2 x + 1\right )^{\frac{15}{2}}}{128} - \frac{4177401 \left (- 2 x + 1\right )^{\frac{13}{2}}}{1664} + \frac{9504551 \left (- 2 x + 1\right )^{\frac{11}{2}}}{1408} - \frac{4324397 \left (- 2 x + 1\right )^{\frac{9}{2}}}{384} + \frac{1405173 \left (- 2 x + 1\right )^{\frac{7}{2}}}{128} - \frac{3195731 \left (- 2 x + 1\right )^{\frac{5}{2}}}{640} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

10125*(-2*x + 1)**(19/2)/2432 - 161325*(-2*x + 1)**(17/2)/2176 + 73431*(-2*x + 1
)**(15/2)/128 - 4177401*(-2*x + 1)**(13/2)/1664 + 9504551*(-2*x + 1)**(11/2)/140
8 - 4324397*(-2*x + 1)**(9/2)/384 + 1405173*(-2*x + 1)**(7/2)/128 - 3195731*(-2*
x + 1)**(5/2)/640

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GIAC/XCAS [A]  time = 0.211702, size = 1, normalized size = 0.01 \[ \mathit{Done} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Done