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3.1254 \(\int (1-2 x)^2 (2+3 x)^9 (3+5 x)^3 \, dx\)

Optimal. Leaf size=67 \[ \frac{100 (3 x+2)^{15}}{2187}-\frac{1900 (3 x+2)^{14}}{5103}+\frac{8285 (3 x+2)^{13}}{9477}-\frac{4099 (3 x+2)^{12}}{8748}+\frac{763 (3 x+2)^{11}}{8019}-\frac{49 (3 x+2)^{10}}{7290} \]

[Out]

(-49*(2 + 3*x)^10)/7290 + (763*(2 + 3*x)^11)/8019 - (4099*(2 + 3*x)^12)/8748 + (
8285*(2 + 3*x)^13)/9477 - (1900*(2 + 3*x)^14)/5103 + (100*(2 + 3*x)^15)/2187

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Rubi [A]  time = 0.128812, antiderivative size = 67, 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 \[ \frac{100 (3 x+2)^{15}}{2187}-\frac{1900 (3 x+2)^{14}}{5103}+\frac{8285 (3 x+2)^{13}}{9477}-\frac{4099 (3 x+2)^{12}}{8748}+\frac{763 (3 x+2)^{11}}{8019}-\frac{49 (3 x+2)^{10}}{7290} \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^2*(2 + 3*x)^9*(3 + 5*x)^3,x]

[Out]

(-49*(2 + 3*x)^10)/7290 + (763*(2 + 3*x)^11)/8019 - (4099*(2 + 3*x)^12)/8748 + (
8285*(2 + 3*x)^13)/9477 - (1900*(2 + 3*x)^14)/5103 + (100*(2 + 3*x)^15)/2187

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Rubi in Sympy [A]  time = 17.1875, size = 60, normalized size = 0.9 \[ \frac{100 \left (3 x + 2\right )^{15}}{2187} - \frac{1900 \left (3 x + 2\right )^{14}}{5103} + \frac{8285 \left (3 x + 2\right )^{13}}{9477} - \frac{4099 \left (3 x + 2\right )^{12}}{8748} + \frac{763 \left (3 x + 2\right )^{11}}{8019} - \frac{49 \left (3 x + 2\right )^{10}}{7290} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2*(2+3*x)**9*(3+5*x)**3,x)

[Out]

100*(3*x + 2)**15/2187 - 1900*(3*x + 2)**14/5103 + 8285*(3*x + 2)**13/9477 - 409
9*(3*x + 2)**12/8748 + 763*(3*x + 2)**11/8019 - 49*(3*x + 2)**10/7290

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Mathematica [A]  time = 0.00430057, size = 90, normalized size = 1.34 \[ 656100 x^{15}+\frac{33461100 x^{14}}{7}+\frac{200077695 x^{13}}{13}+\frac{113029263 x^{12}}{4}+\frac{342976275 x^{11}}{11}+\frac{182657511 x^{10}}{10}-180666 x^9-9703638 x^8-\frac{55216512 x^7}{7}-\frac{7363312 x^6}{3}+\frac{2732864 x^5}{5}+871936 x^4+400128 x^3+100224 x^2+13824 x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)^2*(2 + 3*x)^9*(3 + 5*x)^3,x]

[Out]

13824*x + 100224*x^2 + 400128*x^3 + 871936*x^4 + (2732864*x^5)/5 - (7363312*x^6)
/3 - (55216512*x^7)/7 - 9703638*x^8 - 180666*x^9 + (182657511*x^10)/10 + (342976
275*x^11)/11 + (113029263*x^12)/4 + (200077695*x^13)/13 + (33461100*x^14)/7 + 65
6100*x^15

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Maple [A]  time = 0.003, size = 75, normalized size = 1.1 \[ 656100\,{x}^{15}+{\frac{33461100\,{x}^{14}}{7}}+{\frac{200077695\,{x}^{13}}{13}}+{\frac{113029263\,{x}^{12}}{4}}+{\frac{342976275\,{x}^{11}}{11}}+{\frac{182657511\,{x}^{10}}{10}}-180666\,{x}^{9}-9703638\,{x}^{8}-{\frac{55216512\,{x}^{7}}{7}}-{\frac{7363312\,{x}^{6}}{3}}+{\frac{2732864\,{x}^{5}}{5}}+871936\,{x}^{4}+400128\,{x}^{3}+100224\,{x}^{2}+13824\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(2+3*x)^9*(3+5*x)^3,x)

[Out]

656100*x^15+33461100/7*x^14+200077695/13*x^13+113029263/4*x^12+342976275/11*x^11
+182657511/10*x^10-180666*x^9-9703638*x^8-55216512/7*x^7-7363312/3*x^6+2732864/5
*x^5+871936*x^4+400128*x^3+100224*x^2+13824*x

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Maxima [A]  time = 1.34482, size = 100, normalized size = 1.49 \[ 656100 \, x^{15} + \frac{33461100}{7} \, x^{14} + \frac{200077695}{13} \, x^{13} + \frac{113029263}{4} \, x^{12} + \frac{342976275}{11} \, x^{11} + \frac{182657511}{10} \, x^{10} - 180666 \, x^{9} - 9703638 \, x^{8} - \frac{55216512}{7} \, x^{7} - \frac{7363312}{3} \, x^{6} + \frac{2732864}{5} \, x^{5} + 871936 \, x^{4} + 400128 \, x^{3} + 100224 \, x^{2} + 13824 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^3*(3*x + 2)^9*(2*x - 1)^2,x, algorithm="maxima")

[Out]

656100*x^15 + 33461100/7*x^14 + 200077695/13*x^13 + 113029263/4*x^12 + 342976275
/11*x^11 + 182657511/10*x^10 - 180666*x^9 - 9703638*x^8 - 55216512/7*x^7 - 73633
12/3*x^6 + 2732864/5*x^5 + 871936*x^4 + 400128*x^3 + 100224*x^2 + 13824*x

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Fricas [A]  time = 0.176337, size = 1, normalized size = 0.01 \[ 656100 x^{15} + \frac{33461100}{7} x^{14} + \frac{200077695}{13} x^{13} + \frac{113029263}{4} x^{12} + \frac{342976275}{11} x^{11} + \frac{182657511}{10} x^{10} - 180666 x^{9} - 9703638 x^{8} - \frac{55216512}{7} x^{7} - \frac{7363312}{3} x^{6} + \frac{2732864}{5} x^{5} + 871936 x^{4} + 400128 x^{3} + 100224 x^{2} + 13824 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^3*(3*x + 2)^9*(2*x - 1)^2,x, algorithm="fricas")

[Out]

656100*x^15 + 33461100/7*x^14 + 200077695/13*x^13 + 113029263/4*x^12 + 342976275
/11*x^11 + 182657511/10*x^10 - 180666*x^9 - 9703638*x^8 - 55216512/7*x^7 - 73633
12/3*x^6 + 2732864/5*x^5 + 871936*x^4 + 400128*x^3 + 100224*x^2 + 13824*x

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Sympy [A]  time = 0.138031, size = 87, normalized size = 1.3 \[ 656100 x^{15} + \frac{33461100 x^{14}}{7} + \frac{200077695 x^{13}}{13} + \frac{113029263 x^{12}}{4} + \frac{342976275 x^{11}}{11} + \frac{182657511 x^{10}}{10} - 180666 x^{9} - 9703638 x^{8} - \frac{55216512 x^{7}}{7} - \frac{7363312 x^{6}}{3} + \frac{2732864 x^{5}}{5} + 871936 x^{4} + 400128 x^{3} + 100224 x^{2} + 13824 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2*(2+3*x)**9*(3+5*x)**3,x)

[Out]

656100*x**15 + 33461100*x**14/7 + 200077695*x**13/13 + 113029263*x**12/4 + 34297
6275*x**11/11 + 182657511*x**10/10 - 180666*x**9 - 9703638*x**8 - 55216512*x**7/
7 - 7363312*x**6/3 + 2732864*x**5/5 + 871936*x**4 + 400128*x**3 + 100224*x**2 +
13824*x

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GIAC/XCAS [A]  time = 0.222732, size = 100, normalized size = 1.49 \[ 656100 \, x^{15} + \frac{33461100}{7} \, x^{14} + \frac{200077695}{13} \, x^{13} + \frac{113029263}{4} \, x^{12} + \frac{342976275}{11} \, x^{11} + \frac{182657511}{10} \, x^{10} - 180666 \, x^{9} - 9703638 \, x^{8} - \frac{55216512}{7} \, x^{7} - \frac{7363312}{3} \, x^{6} + \frac{2732864}{5} \, x^{5} + 871936 \, x^{4} + 400128 \, x^{3} + 100224 \, x^{2} + 13824 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^3*(3*x + 2)^9*(2*x - 1)^2,x, algorithm="giac")

[Out]

656100*x^15 + 33461100/7*x^14 + 200077695/13*x^13 + 113029263/4*x^12 + 342976275
/11*x^11 + 182657511/10*x^10 - 180666*x^9 - 9703638*x^8 - 55216512/7*x^7 - 73633
12/3*x^6 + 2732864/5*x^5 + 871936*x^4 + 400128*x^3 + 100224*x^2 + 13824*x

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