3.1241 \(\int (1-2 x)^2 (2+3 x)^3 (3+5 x)^2 \, dx\)

Optimal. Leaf size=56 \[ \frac{25}{486} (3 x+2)^8-\frac{740 (3 x+2)^7}{1701}+\frac{503}{486} (3 x+2)^6-\frac{518 (3 x+2)^5}{1215}+\frac{49}{972} (3 x+2)^4 \]

[Out]

(49*(2 + 3*x)^4)/972 - (518*(2 + 3*x)^5)/1215 + (503*(2 + 3*x)^6)/486 - (740*(2
+ 3*x)^7)/1701 + (25*(2 + 3*x)^8)/486

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Rubi [A]  time = 0.0865532, antiderivative size = 56, 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 \[ \frac{25}{486} (3 x+2)^8-\frac{740 (3 x+2)^7}{1701}+\frac{503}{486} (3 x+2)^6-\frac{518 (3 x+2)^5}{1215}+\frac{49}{972} (3 x+2)^4 \]

Antiderivative was successfully verified.

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

[Out]

(49*(2 + 3*x)^4)/972 - (518*(2 + 3*x)^5)/1215 + (503*(2 + 3*x)^6)/486 - (740*(2
+ 3*x)^7)/1701 + (25*(2 + 3*x)^8)/486

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{675 x^{8}}{2} + \frac{5940 x^{7}}{7} + \frac{1029 x^{6}}{2} - \frac{1828 x^{5}}{5} - \frac{2045 x^{4}}{4} - \frac{202 x^{3}}{3} + 72 x + 276 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675*x**8/2 + 5940*x**7/7 + 1029*x**6/2 - 1828*x**5/5 - 2045*x**4/4 - 202*x**3/3
+ 72*x + 276*Integral(x, x)

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Mathematica [A]  time = 0.00293264, size = 51, normalized size = 0.91 \[ \frac{675 x^8}{2}+\frac{5940 x^7}{7}+\frac{1029 x^6}{2}-\frac{1828 x^5}{5}-\frac{2045 x^4}{4}-\frac{202 x^3}{3}+138 x^2+72 x \]

Antiderivative was successfully verified.

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

[Out]

72*x + 138*x^2 - (202*x^3)/3 - (2045*x^4)/4 - (1828*x^5)/5 + (1029*x^6)/2 + (594
0*x^7)/7 + (675*x^8)/2

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Maple [A]  time = 0., size = 40, normalized size = 0.7 \[{\frac{675\,{x}^{8}}{2}}+{\frac{5940\,{x}^{7}}{7}}+{\frac{1029\,{x}^{6}}{2}}-{\frac{1828\,{x}^{5}}{5}}-{\frac{2045\,{x}^{4}}{4}}-{\frac{202\,{x}^{3}}{3}}+138\,{x}^{2}+72\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675/2*x^8+5940/7*x^7+1029/2*x^6-1828/5*x^5-2045/4*x^4-202/3*x^3+138*x^2+72*x

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Maxima [A]  time = 1.35345, size = 53, normalized size = 0.95 \[ \frac{675}{2} \, x^{8} + \frac{5940}{7} \, x^{7} + \frac{1029}{2} \, x^{6} - \frac{1828}{5} \, x^{5} - \frac{2045}{4} \, x^{4} - \frac{202}{3} \, x^{3} + 138 \, x^{2} + 72 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675/2*x^8 + 5940/7*x^7 + 1029/2*x^6 - 1828/5*x^5 - 2045/4*x^4 - 202/3*x^3 + 138*
x^2 + 72*x

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Fricas [A]  time = 0.191284, size = 1, normalized size = 0.02 \[ \frac{675}{2} x^{8} + \frac{5940}{7} x^{7} + \frac{1029}{2} x^{6} - \frac{1828}{5} x^{5} - \frac{2045}{4} x^{4} - \frac{202}{3} x^{3} + 138 x^{2} + 72 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675/2*x^8 + 5940/7*x^7 + 1029/2*x^6 - 1828/5*x^5 - 2045/4*x^4 - 202/3*x^3 + 138*
x^2 + 72*x

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Sympy [A]  time = 0.093048, size = 48, normalized size = 0.86 \[ \frac{675 x^{8}}{2} + \frac{5940 x^{7}}{7} + \frac{1029 x^{6}}{2} - \frac{1828 x^{5}}{5} - \frac{2045 x^{4}}{4} - \frac{202 x^{3}}{3} + 138 x^{2} + 72 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675*x**8/2 + 5940*x**7/7 + 1029*x**6/2 - 1828*x**5/5 - 2045*x**4/4 - 202*x**3/3
+ 138*x**2 + 72*x

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GIAC/XCAS [A]  time = 0.212212, size = 53, normalized size = 0.95 \[ \frac{675}{2} \, x^{8} + \frac{5940}{7} \, x^{7} + \frac{1029}{2} \, x^{6} - \frac{1828}{5} \, x^{5} - \frac{2045}{4} \, x^{4} - \frac{202}{3} \, x^{3} + 138 \, x^{2} + 72 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675/2*x^8 + 5940/7*x^7 + 1029/2*x^6 - 1828/5*x^5 - 2045/4*x^4 - 202/3*x^3 + 138*
x^2 + 72*x