3.1925 \(\int (1-2 x)^{5/2} (2+3 x)^4 (3+5 x)^2 \, dx\)

Optimal. Leaf size=92 \[ -\frac{2025 (1-2 x)^{19/2}}{1216}+\frac{13905}{544} (1-2 x)^{17/2}-\frac{53037}{320} (1-2 x)^{15/2}+\frac{121359}{208} (1-2 x)^{13/2}-\frac{832951}{704} (1-2 x)^{11/2}+\frac{381073}{288} (1-2 x)^{9/2}-\frac{41503}{64} (1-2 x)^{7/2} \]

[Out]

(-41503*(1 - 2*x)^(7/2))/64 + (381073*(1 - 2*x)^(9/2))/288 - (832951*(1 - 2*x)^(
11/2))/704 + (121359*(1 - 2*x)^(13/2))/208 - (53037*(1 - 2*x)^(15/2))/320 + (139
05*(1 - 2*x)^(17/2))/544 - (2025*(1 - 2*x)^(19/2))/1216

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Rubi [A]  time = 0.0718861, antiderivative size = 92, 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 \[ -\frac{2025 (1-2 x)^{19/2}}{1216}+\frac{13905}{544} (1-2 x)^{17/2}-\frac{53037}{320} (1-2 x)^{15/2}+\frac{121359}{208} (1-2 x)^{13/2}-\frac{832951}{704} (1-2 x)^{11/2}+\frac{381073}{288} (1-2 x)^{9/2}-\frac{41503}{64} (1-2 x)^{7/2} \]

Antiderivative was successfully verified.

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

[Out]

(-41503*(1 - 2*x)^(7/2))/64 + (381073*(1 - 2*x)^(9/2))/288 - (832951*(1 - 2*x)^(
11/2))/704 + (121359*(1 - 2*x)^(13/2))/208 - (53037*(1 - 2*x)^(15/2))/320 + (139
05*(1 - 2*x)^(17/2))/544 - (2025*(1 - 2*x)^(19/2))/1216

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Rubi in Sympy [A]  time = 10.2238, size = 82, normalized size = 0.89 \[ - \frac{2025 \left (- 2 x + 1\right )^{\frac{19}{2}}}{1216} + \frac{13905 \left (- 2 x + 1\right )^{\frac{17}{2}}}{544} - \frac{53037 \left (- 2 x + 1\right )^{\frac{15}{2}}}{320} + \frac{121359 \left (- 2 x + 1\right )^{\frac{13}{2}}}{208} - \frac{832951 \left (- 2 x + 1\right )^{\frac{11}{2}}}{704} + \frac{381073 \left (- 2 x + 1\right )^{\frac{9}{2}}}{288} - \frac{41503 \left (- 2 x + 1\right )^{\frac{7}{2}}}{64} \]

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)**2,x)

[Out]

-2025*(-2*x + 1)**(19/2)/1216 + 13905*(-2*x + 1)**(17/2)/544 - 53037*(-2*x + 1)*
*(15/2)/320 + 121359*(-2*x + 1)**(13/2)/208 - 832951*(-2*x + 1)**(11/2)/704 + 38
1073*(-2*x + 1)**(9/2)/288 - 41503*(-2*x + 1)**(7/2)/64

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Mathematica [A]  time = 0.0626914, size = 43, normalized size = 0.47 \[ -\frac{(1-2 x)^{7/2} \left (221524875 x^6+1035520200 x^5+2092364703 x^4+2374399764 x^3+1634664492 x^2+673648856 x+138993368\right )}{2078505} \]

Antiderivative was successfully verified.

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

[Out]

-((1 - 2*x)^(7/2)*(138993368 + 673648856*x + 1634664492*x^2 + 2374399764*x^3 + 2
092364703*x^4 + 1035520200*x^5 + 221524875*x^6))/2078505

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Maple [A]  time = 0.006, size = 40, normalized size = 0.4 \[ -{\frac{221524875\,{x}^{6}[phone]\,{x}^{5}[phone]\,{x}^{4}[phone]\,{x}^{3}[phone]\,{x}^{2}[phone]\,x+138993368}{2078505} \left ( 1-2\,x \right ) ^{{\frac{7}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2078505*(221524875*x^6+1035520200*x^5+2092364703*x^4+2374399764*x^3+163466449
2*x^2+673648856*x+138993368)*(1-2*x)^(7/2)

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Maxima [A]  time = 1.34997, size = 86, normalized size = 0.93 \[ -\frac{2025}{1216} \,{\left (-2 \, x + 1\right )}^{\frac{19}{2}} + \frac{13905}{544} \,{\left (-2 \, x + 1\right )}^{\frac{17}{2}} - \frac{53037}{320} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{121359}{208} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{832951}{704} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{381073}{288} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{41503}{64} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2025/1216*(-2*x + 1)^(19/2) + 13905/544*(-2*x + 1)^(17/2) - 53037/320*(-2*x + 1
)^(15/2) + 121359/208*(-2*x + 1)^(13/2) - 832951/704*(-2*x + 1)^(11/2) + 381073/
288*(-2*x + 1)^(9/2) - 41503/64*(-2*x + 1)^(7/2)

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Fricas [A]  time = 0.23249, size = 73, normalized size = 0.79 \[ \frac{1}{2078505} \,{\left (1772199000 \, x^{9} + 5625863100 \, x^{8} + 5641824474 \, x^{7} - 121581999 \, x^{6} - 3896813214 \, x^{5} - 2072749175 \, x^{4} + 461747860 \, x^{3} + 739308228 \, x^{2} + 160311352 \, x - 138993368\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2078505*(1772199000*x^9 + 5625863100*x^8 + 5641824474*x^7 - 121581999*x^6 - 38
96813214*x^5 - 2072749175*x^4 + 461747860*x^3 + 739308228*x^2 + 160311352*x - 13
8993368)*sqrt(-2*x + 1)

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Sympy [A]  time = 5.73562, size = 82, normalized size = 0.89 \[ - \frac{2025 \left (- 2 x + 1\right )^{\frac{19}{2}}}{1216} + \frac{13905 \left (- 2 x + 1\right )^{\frac{17}{2}}}{544} - \frac{53037 \left (- 2 x + 1\right )^{\frac{15}{2}}}{320} + \frac{121359 \left (- 2 x + 1\right )^{\frac{13}{2}}}{208} - \frac{832951 \left (- 2 x + 1\right )^{\frac{11}{2}}}{704} + \frac{381073 \left (- 2 x + 1\right )^{\frac{9}{2}}}{288} - \frac{41503 \left (- 2 x + 1\right )^{\frac{7}{2}}}{64} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2025*(-2*x + 1)**(19/2)/1216 + 13905*(-2*x + 1)**(17/2)/544 - 53037*(-2*x + 1)*
*(15/2)/320 + 121359*(-2*x + 1)**(13/2)/208 - 832951*(-2*x + 1)**(11/2)/704 + 38
1073*(-2*x + 1)**(9/2)/288 - 41503*(-2*x + 1)**(7/2)/64

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GIAC/XCAS [A]  time = 0.23805, size = 1, normalized size = 0.01 \[ \mathit{Done} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Done