3.1345 \(\int (1-2 x)^3 (2+3 x) (3+5 x)^2 \, dx\)

Optimal. Leaf size=45 \[ \frac{75}{112} (1-2 x)^7-\frac{505}{96} (1-2 x)^6+\frac{1133}{80} (1-2 x)^5-\frac{847}{64} (1-2 x)^4 \]

[Out]

(-847*(1 - 2*x)^4)/64 + (1133*(1 - 2*x)^5)/80 - (505*(1 - 2*x)^6)/96 + (75*(1 -
2*x)^7)/112

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Rubi [A]  time = 0.0624844, antiderivative size = 45, 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 \[ \frac{75}{112} (1-2 x)^7-\frac{505}{96} (1-2 x)^6+\frac{1133}{80} (1-2 x)^5-\frac{847}{64} (1-2 x)^4 \]

Antiderivative was successfully verified.

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

[Out]

(-847*(1 - 2*x)^4)/64 + (1133*(1 - 2*x)^5)/80 - (505*(1 - 2*x)^6)/96 + (75*(1 -
2*x)^7)/112

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{600 x^{7}}{7} - \frac{110 x^{6}}{3} + \frac{534 x^{5}}{5} + \frac{135 x^{4}}{4} - \frac{166 x^{3}}{3} + 18 x - 21 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-600*x**7/7 - 110*x**6/3 + 534*x**5/5 + 135*x**4/4 - 166*x**3/3 + 18*x - 21*Inte
gral(x, x)

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Mathematica [A]  time = 0.00144568, size = 46, normalized size = 1.02 \[ -\frac{600 x^7}{7}-\frac{110 x^6}{3}+\frac{534 x^5}{5}+\frac{135 x^4}{4}-\frac{166 x^3}{3}-\frac{21 x^2}{2}+18 x \]

Antiderivative was successfully verified.

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

[Out]

18*x - (21*x^2)/2 - (166*x^3)/3 + (135*x^4)/4 + (534*x^5)/5 - (110*x^6)/3 - (600
*x^7)/7

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Maple [A]  time = 0.001, size = 35, normalized size = 0.8 \[ -{\frac{600\,{x}^{7}}{7}}-{\frac{110\,{x}^{6}}{3}}+{\frac{534\,{x}^{5}}{5}}+{\frac{135\,{x}^{4}}{4}}-{\frac{166\,{x}^{3}}{3}}-{\frac{21\,{x}^{2}}{2}}+18\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-600/7*x^7-110/3*x^6+534/5*x^5+135/4*x^4-166/3*x^3-21/2*x^2+18*x

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Maxima [A]  time = 1.35265, size = 46, normalized size = 1.02 \[ -\frac{600}{7} \, x^{7} - \frac{110}{3} \, x^{6} + \frac{534}{5} \, x^{5} + \frac{135}{4} \, x^{4} - \frac{166}{3} \, x^{3} - \frac{21}{2} \, x^{2} + 18 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-600/7*x^7 - 110/3*x^6 + 534/5*x^5 + 135/4*x^4 - 166/3*x^3 - 21/2*x^2 + 18*x

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Fricas [A]  time = 0.184152, size = 1, normalized size = 0.02 \[ -\frac{600}{7} x^{7} - \frac{110}{3} x^{6} + \frac{534}{5} x^{5} + \frac{135}{4} x^{4} - \frac{166}{3} x^{3} - \frac{21}{2} x^{2} + 18 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-600/7*x^7 - 110/3*x^6 + 534/5*x^5 + 135/4*x^4 - 166/3*x^3 - 21/2*x^2 + 18*x

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Sympy [A]  time = 0.088277, size = 42, normalized size = 0.93 \[ - \frac{600 x^{7}}{7} - \frac{110 x^{6}}{3} + \frac{534 x^{5}}{5} + \frac{135 x^{4}}{4} - \frac{166 x^{3}}{3} - \frac{21 x^{2}}{2} + 18 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-600*x**7/7 - 110*x**6/3 + 534*x**5/5 + 135*x**4/4 - 166*x**3/3 - 21*x**2/2 + 18
*x

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GIAC/XCAS [A]  time = 0.204293, size = 46, normalized size = 1.02 \[ -\frac{600}{7} \, x^{7} - \frac{110}{3} \, x^{6} + \frac{534}{5} \, x^{5} + \frac{135}{4} \, x^{4} - \frac{166}{3} \, x^{3} - \frac{21}{2} \, x^{2} + 18 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-600/7*x^7 - 110/3*x^6 + 534/5*x^5 + 135/4*x^4 - 166/3*x^3 - 21/2*x^2 + 18*x