3.1240 \(\int (1-2 x)^2 (2+3 x)^4 (3+5 x)^2 \, dx\)

Optimal. Leaf size=56 \[ \frac{100 (3 x+2)^9}{2187}-\frac{185}{486} (3 x+2)^8+\frac{503}{567} (3 x+2)^7-\frac{259}{729} (3 x+2)^6+\frac{49 (3 x+2)^5}{1215} \]

[Out]

(49*(2 + 3*x)^5)/1215 - (259*(2 + 3*x)^6)/729 + (503*(2 + 3*x)^7)/567 - (185*(2
+ 3*x)^8)/486 + (100*(2 + 3*x)^9)/2187

_______________________________________________________________________________________

Rubi [A]  time = 0.0876613, 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 \[ \frac{100 (3 x+2)^9}{2187}-\frac{185}{486} (3 x+2)^8+\frac{503}{567} (3 x+2)^7-\frac{259}{729} (3 x+2)^6+\frac{49 (3 x+2)^5}{1215} \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^2,x]

[Out]

(49*(2 + 3*x)^5)/1215 - (259*(2 + 3*x)^6)/729 + (503*(2 + 3*x)^7)/567 - (185*(2
+ 3*x)^8)/486 + (100*(2 + 3*x)^9)/2187

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ 900 x^{9} + \frac{5805 x^{8}}{2} + \frac{21141 x^{7}}{7} + 115 x^{6} - \frac{9791 x^{5}}{5} - 1174 x^{4} + \frac{424 x^{3}}{3} + 144 x + 768 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2*(2+3*x)**4*(3+5*x)**2,x)

[Out]

900*x**9 + 5805*x**8/2 + 21141*x**7/7 + 115*x**6 - 9791*x**5/5 - 1174*x**4 + 424
*x**3/3 + 144*x + 768*Integral(x, x)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0030456, size = 52, normalized size = 0.93 \[ 900 x^9+\frac{5805 x^8}{2}+\frac{21141 x^7}{7}+115 x^6-\frac{9791 x^5}{5}-1174 x^4+\frac{424 x^3}{3}+384 x^2+144 x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^2,x]

[Out]

144*x + 384*x^2 + (424*x^3)/3 - 1174*x^4 - (9791*x^5)/5 + 115*x^6 + (21141*x^7)/
7 + (5805*x^8)/2 + 900*x^9

_______________________________________________________________________________________

Maple [A]  time = 0., size = 45, normalized size = 0.8 \[ 900\,{x}^{9}+{\frac{5805\,{x}^{8}}{2}}+{\frac{21141\,{x}^{7}}{7}}+115\,{x}^{6}-{\frac{9791\,{x}^{5}}{5}}-1174\,{x}^{4}+{\frac{424\,{x}^{3}}{3}}+384\,{x}^{2}+144\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(2+3*x)^4*(3+5*x)^2,x)

[Out]

900*x^9+5805/2*x^8+21141/7*x^7+115*x^6-9791/5*x^5-1174*x^4+424/3*x^3+384*x^2+144
*x

_______________________________________________________________________________________

Maxima [A]  time = 1.34828, size = 59, normalized size = 1.05 \[ 900 \, x^{9} + \frac{5805}{2} \, x^{8} + \frac{21141}{7} \, x^{7} + 115 \, x^{6} - \frac{9791}{5} \, x^{5} - 1174 \, x^{4} + \frac{424}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^4*(2*x - 1)^2,x, algorithm="maxima")

[Out]

900*x^9 + 5805/2*x^8 + 21141/7*x^7 + 115*x^6 - 9791/5*x^5 - 1174*x^4 + 424/3*x^3
+ 384*x^2 + 144*x

_______________________________________________________________________________________

Fricas [A]  time = 0.181961, size = 1, normalized size = 0.02 \[ 900 x^{9} + \frac{5805}{2} x^{8} + \frac{21141}{7} x^{7} + 115 x^{6} - \frac{9791}{5} x^{5} - 1174 x^{4} + \frac{424}{3} x^{3} + 384 x^{2} + 144 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^4*(2*x - 1)^2,x, algorithm="fricas")

[Out]

900*x^9 + 5805/2*x^8 + 21141/7*x^7 + 115*x^6 - 9791/5*x^5 - 1174*x^4 + 424/3*x^3
+ 384*x^2 + 144*x

_______________________________________________________________________________________

Sympy [A]  time = 0.102483, size = 49, normalized size = 0.88 \[ 900 x^{9} + \frac{5805 x^{8}}{2} + \frac{21141 x^{7}}{7} + 115 x^{6} - \frac{9791 x^{5}}{5} - 1174 x^{4} + \frac{424 x^{3}}{3} + 384 x^{2} + 144 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2*(2+3*x)**4*(3+5*x)**2,x)

[Out]

900*x**9 + 5805*x**8/2 + 21141*x**7/7 + 115*x**6 - 9791*x**5/5 - 1174*x**4 + 424
*x**3/3 + 384*x**2 + 144*x

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.207567, size = 59, normalized size = 1.05 \[ 900 \, x^{9} + \frac{5805}{2} \, x^{8} + \frac{21141}{7} \, x^{7} + 115 \, x^{6} - \frac{9791}{5} \, x^{5} - 1174 \, x^{4} + \frac{424}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^4*(2*x - 1)^2,x, algorithm="giac")

[Out]

900*x^9 + 5805/2*x^8 + 21141/7*x^7 + 115*x^6 - 9791/5*x^5 - 1174*x^4 + 424/3*x^3
+ 384*x^2 + 144*x