3.1912 \(\int (1-2 x)^{5/2} (2+3 x)^5 (3+5 x) \, dx\)

Optimal. Leaf size=92 \[ -\frac{1215 (1-2 x)^{19/2}}{1216}+\frac{1053}{68} (1-2 x)^{17/2}-\frac{6489}{64} (1-2 x)^{15/2}+\frac{37485}{104} (1-2 x)^{13/2}-\frac{519645}{704} (1-2 x)^{11/2}+\frac{60025}{72} (1-2 x)^{9/2}-\frac{26411}{64} (1-2 x)^{7/2} \]

[Out]

(-26411*(1 - 2*x)^(7/2))/64 + (60025*(1 - 2*x)^(9/2))/72 - (519645*(1 - 2*x)^(11
/2))/704 + (37485*(1 - 2*x)^(13/2))/104 - (6489*(1 - 2*x)^(15/2))/64 + (1053*(1
- 2*x)^(17/2))/68 - (1215*(1 - 2*x)^(19/2))/1216

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Rubi [A]  time = 0.0684792, antiderivative size = 92, 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 \[ -\frac{1215 (1-2 x)^{19/2}}{1216}+\frac{1053}{68} (1-2 x)^{17/2}-\frac{6489}{64} (1-2 x)^{15/2}+\frac{37485}{104} (1-2 x)^{13/2}-\frac{519645}{704} (1-2 x)^{11/2}+\frac{60025}{72} (1-2 x)^{9/2}-\frac{26411}{64} (1-2 x)^{7/2} \]

Antiderivative was successfully verified.

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

[Out]

(-26411*(1 - 2*x)^(7/2))/64 + (60025*(1 - 2*x)^(9/2))/72 - (519645*(1 - 2*x)^(11
/2))/704 + (37485*(1 - 2*x)^(13/2))/104 - (6489*(1 - 2*x)^(15/2))/64 + (1053*(1
- 2*x)^(17/2))/68 - (1215*(1 - 2*x)^(19/2))/1216

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Rubi in Sympy [A]  time = 9.81639, size = 82, normalized size = 0.89 \[ - \frac{1215 \left (- 2 x + 1\right )^{\frac{19}{2}}}{1216} + \frac{1053 \left (- 2 x + 1\right )^{\frac{17}{2}}}{68} - \frac{6489 \left (- 2 x + 1\right )^{\frac{15}{2}}}{64} + \frac{37485 \left (- 2 x + 1\right )^{\frac{13}{2}}}{104} - \frac{519645 \left (- 2 x + 1\right )^{\frac{11}{2}}}{704} + \frac{60025 \left (- 2 x + 1\right )^{\frac{9}{2}}}{72} - \frac{26411 \left (- 2 x + 1\right )^{\frac{7}{2}}}{64} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1215*(-2*x + 1)**(19/2)/1216 + 1053*(-2*x + 1)**(17/2)/68 - 6489*(-2*x + 1)**(1
5/2)/64 + 37485*(-2*x + 1)**(13/2)/104 - 519645*(-2*x + 1)**(11/2)/704 + 60025*(
-2*x + 1)**(9/2)/72 - 26411*(-2*x + 1)**(7/2)/64

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Mathematica [A]  time = 0.0519467, size = 43, normalized size = 0.47 \[ -\frac{(1-2 x)^{7/2} \left (26582985 x^6+126243117 x^5+259076961 x^4+298438668 x^3+208370124 x^2+86950792 x+18122584\right )}{415701} \]

Antiderivative was successfully verified.

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

[Out]

-((1 - 2*x)^(7/2)*(18122584 + 86950792*x + 208370124*x^2 + 298438668*x^3 + 25907
6961*x^4 + 126243117*x^5 + 26582985*x^6))/415701

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Maple [A]  time = 0.007, size = 40, normalized size = 0.4 \[ -{\frac{26582985\,{x}^{6}[phone]\,{x}^{5}[phone]\,{x}^{4}[phone]\,{x}^{3}[phone]\,{x}^{2}[phone]\,x+18122584}{415701} \left ( 1-2\,x \right ) ^{{\frac{7}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/415701*(26582985*x^6+126243117*x^5+259076961*x^4+298438668*x^3+208370124*x^2+
86950792*x+18122584)*(1-2*x)^(7/2)

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Maxima [A]  time = 1.33681, size = 86, normalized size = 0.93 \[ -\frac{1215}{1216} \,{\left (-2 \, x + 1\right )}^{\frac{19}{2}} + \frac{1053}{68} \,{\left (-2 \, x + 1\right )}^{\frac{17}{2}} - \frac{6489}{64} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{37485}{104} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{519645}{704} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{60025}{72} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{26411}{64} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1215/1216*(-2*x + 1)^(19/2) + 1053/68*(-2*x + 1)^(17/2) - 6489/64*(-2*x + 1)^(1
5/2) + 37485/104*(-2*x + 1)^(13/2) - 519645/704*(-2*x + 1)^(11/2) + 60025/72*(-2
*x + 1)^(9/2) - 26411/64*(-2*x + 1)^(7/2)

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Fricas [A]  time = 0.225345, size = 73, normalized size = 0.79 \[ \frac{1}{415701} \,{\left (212663880 \, x^{9} + 690949116 \, x^{8} + 717196194 \, x^{7} + 9461529 \, x^{6} - 486084375 \, x^{5} - 273280105 \, x^{4} + 53353244 \, x^{3} + 95863620 \, x^{2} + 21784712 \, x - 18122584\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/415701*(212663880*x^9 + 690949116*x^8 + 717196194*x^7 + 9461529*x^6 - 48608437
5*x^5 - 273280105*x^4 + 53353244*x^3 + 95863620*x^2 + 21784712*x - 18122584)*sqr
t(-2*x + 1)

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Sympy [A]  time = 5.81371, size = 82, normalized size = 0.89 \[ - \frac{1215 \left (- 2 x + 1\right )^{\frac{19}{2}}}{1216} + \frac{1053 \left (- 2 x + 1\right )^{\frac{17}{2}}}{68} - \frac{6489 \left (- 2 x + 1\right )^{\frac{15}{2}}}{64} + \frac{37485 \left (- 2 x + 1\right )^{\frac{13}{2}}}{104} - \frac{519645 \left (- 2 x + 1\right )^{\frac{11}{2}}}{704} + \frac{60025 \left (- 2 x + 1\right )^{\frac{9}{2}}}{72} - \frac{26411 \left (- 2 x + 1\right )^{\frac{7}{2}}}{64} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1215*(-2*x + 1)**(19/2)/1216 + 1053*(-2*x + 1)**(17/2)/68 - 6489*(-2*x + 1)**(1
5/2)/64 + 37485*(-2*x + 1)**(13/2)/104 - 519645*(-2*x + 1)**(11/2)/704 + 60025*(
-2*x + 1)**(9/2)/72 - 26411*(-2*x + 1)**(7/2)/64

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GIAC/XCAS [A]  time = 0.21433, size = 1, normalized size = 0.01 \[ \mathit{Done} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Done