3.1324 \(\int (1-2 x)^3 (2+3 x)^5 (3+5 x) \, dx\)

Optimal. Leaf size=56 \[ -\frac{4}{243} (3 x+2)^{10}+\frac{428 (3 x+2)^9}{2187}-\frac{259}{324} (3 x+2)^8+\frac{287}{243} (3 x+2)^7-\frac{343 (3 x+2)^6}{1458} \]

[Out]

(-343*(2 + 3*x)^6)/1458 + (287*(2 + 3*x)^7)/243 - (259*(2 + 3*x)^8)/324 + (428*(
2 + 3*x)^9)/2187 - (4*(2 + 3*x)^10)/243

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Rubi [A]  time = 0.0855785, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{4}{243} (3 x+2)^{10}+\frac{428 (3 x+2)^9}{2187}-\frac{259}{324} (3 x+2)^8+\frac{287}{243} (3 x+2)^7-\frac{343 (3 x+2)^6}{1458} \]

Antiderivative was successfully verified.

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

[Out]

(-343*(2 + 3*x)^6)/1458 + (287*(2 + 3*x)^7)/243 - (259*(2 + 3*x)^8)/324 + (428*(
2 + 3*x)^9)/2187 - (4*(2 + 3*x)^10)/243

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - 972 x^{10} - 2628 x^{9} - \frac{6291 x^{8}}{4} + 1683 x^{7} + \frac{4333 x^{6}}{2} + 14 x^{5} - 882 x^{4} - 256 x^{3} + 96 x + 304 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-972*x**10 - 2628*x**9 - 6291*x**8/4 + 1683*x**7 + 4333*x**6/2 + 14*x**5 - 882*x
**4 - 256*x**3 + 96*x + 304*Integral(x, x)

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Mathematica [A]  time = 0.00335886, size = 53, normalized size = 0.95 \[ -972 x^{10}-2628 x^9-\frac{6291 x^8}{4}+1683 x^7+\frac{4333 x^6}{2}+14 x^5-882 x^4-256 x^3+152 x^2+96 x \]

Antiderivative was successfully verified.

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

[Out]

96*x + 152*x^2 - 256*x^3 - 882*x^4 + 14*x^5 + (4333*x^6)/2 + 1683*x^7 - (6291*x^
8)/4 - 2628*x^9 - 972*x^10

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Maple [A]  time = 0.001, size = 50, normalized size = 0.9 \[ -972\,{x}^{10}-2628\,{x}^{9}-{\frac{6291\,{x}^{8}}{4}}+1683\,{x}^{7}+{\frac{4333\,{x}^{6}}{2}}+14\,{x}^{5}-882\,{x}^{4}-256\,{x}^{3}+152\,{x}^{2}+96\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-972*x^10-2628*x^9-6291/4*x^8+1683*x^7+4333/2*x^6+14*x^5-882*x^4-256*x^3+152*x^2
+96*x

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Maxima [A]  time = 1.3571, size = 66, normalized size = 1.18 \[ -972 \, x^{10} - 2628 \, x^{9} - \frac{6291}{4} \, x^{8} + 1683 \, x^{7} + \frac{4333}{2} \, x^{6} + 14 \, x^{5} - 882 \, x^{4} - 256 \, x^{3} + 152 \, x^{2} + 96 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-972*x^10 - 2628*x^9 - 6291/4*x^8 + 1683*x^7 + 4333/2*x^6 + 14*x^5 - 882*x^4 - 2
56*x^3 + 152*x^2 + 96*x

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Fricas [A]  time = 0.189122, size = 1, normalized size = 0.02 \[ -972 x^{10} - 2628 x^{9} - \frac{6291}{4} x^{8} + 1683 x^{7} + \frac{4333}{2} x^{6} + 14 x^{5} - 882 x^{4} - 256 x^{3} + 152 x^{2} + 96 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-972*x^10 - 2628*x^9 - 6291/4*x^8 + 1683*x^7 + 4333/2*x^6 + 14*x^5 - 882*x^4 - 2
56*x^3 + 152*x^2 + 96*x

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Sympy [A]  time = 0.104762, size = 51, normalized size = 0.91 \[ - 972 x^{10} - 2628 x^{9} - \frac{6291 x^{8}}{4} + 1683 x^{7} + \frac{4333 x^{6}}{2} + 14 x^{5} - 882 x^{4} - 256 x^{3} + 152 x^{2} + 96 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-972*x**10 - 2628*x**9 - 6291*x**8/4 + 1683*x**7 + 4333*x**6/2 + 14*x**5 - 882*x
**4 - 256*x**3 + 152*x**2 + 96*x

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GIAC/XCAS [A]  time = 0.210904, size = 66, normalized size = 1.18 \[ -972 \, x^{10} - 2628 \, x^{9} - \frac{6291}{4} \, x^{8} + 1683 \, x^{7} + \frac{4333}{2} \, x^{6} + 14 \, x^{5} - 882 \, x^{4} - 256 \, x^{3} + 152 \, x^{2} + 96 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-972*x^10 - 2628*x^9 - 6291/4*x^8 + 1683*x^7 + 4333/2*x^6 + 14*x^5 - 882*x^4 - 2
56*x^3 + 152*x^2 + 96*x