3.52 \(\int \left (1+4 x+4 x^2+4 x^4\right )^3 \, dx\)

Optimal. Leaf size=69 \[ \frac{64 x^{13}}{13}+\frac{192 x^{11}}{11}+\frac{96 x^{10}}{5}+\frac{80 x^9}{3}+48 x^8+\frac{352 x^7}{7}+48 x^6+\frac{252 x^5}{5}+40 x^4+20 x^3+6 x^2+x \]

[Out]

x + 6*x^2 + 20*x^3 + 40*x^4 + (252*x^5)/5 + 48*x^6 + (352*x^7)/7 + 48*x^8 + (80*
x^9)/3 + (96*x^10)/5 + (192*x^11)/11 + (64*x^13)/13

_______________________________________________________________________________________

Rubi [A]  time = 0.0415652, antiderivative size = 69, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{64 x^{13}}{13}+\frac{192 x^{11}}{11}+\frac{96 x^{10}}{5}+\frac{80 x^9}{3}+48 x^8+\frac{352 x^7}{7}+48 x^6+\frac{252 x^5}{5}+40 x^4+20 x^3+6 x^2+x \]

Antiderivative was successfully verified.

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

[Out]

x + 6*x^2 + 20*x^3 + 40*x^4 + (252*x^5)/5 + 48*x^6 + (352*x^7)/7 + 48*x^8 + (80*
x^9)/3 + (96*x^10)/5 + (192*x^11)/11 + (64*x^13)/13

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 31.7697, size = 66, normalized size = 0.96 \[ \frac{64 x^{13}}{13} + \frac{192 x^{11}}{11} + \frac{96 x^{10}}{5} + \frac{80 x^{9}}{3} + 48 x^{8} + \frac{352 x^{7}}{7} + 48 x^{6} + \frac{252 x^{5}}{5} + 40 x^{4} + 20 x^{3} + 6 x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

64*x**13/13 + 192*x**11/11 + 96*x**10/5 + 80*x**9/3 + 48*x**8 + 352*x**7/7 + 48*
x**6 + 252*x**5/5 + 40*x**4 + 20*x**3 + 6*x**2 + x

_______________________________________________________________________________________

Mathematica [A]  time = 0.00142392, size = 69, normalized size = 1. \[ \frac{64 x^{13}}{13}+\frac{192 x^{11}}{11}+\frac{96 x^{10}}{5}+\frac{80 x^9}{3}+48 x^8+\frac{352 x^7}{7}+48 x^6+\frac{252 x^5}{5}+40 x^4+20 x^3+6 x^2+x \]

Antiderivative was successfully verified.

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

[Out]

x + 6*x^2 + 20*x^3 + 40*x^4 + (252*x^5)/5 + 48*x^6 + (352*x^7)/7 + 48*x^8 + (80*
x^9)/3 + (96*x^10)/5 + (192*x^11)/11 + (64*x^13)/13

_______________________________________________________________________________________

Maple [A]  time = 0.002, size = 58, normalized size = 0.8 \[ x+6\,{x}^{2}+20\,{x}^{3}+40\,{x}^{4}+{\frac{252\,{x}^{5}}{5}}+48\,{x}^{6}+{\frac{352\,{x}^{7}}{7}}+48\,{x}^{8}+{\frac{80\,{x}^{9}}{3}}+{\frac{96\,{x}^{10}}{5}}+{\frac{192\,{x}^{11}}{11}}+{\frac{64\,{x}^{13}}{13}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((4*x^4+4*x^2+4*x+1)^3,x)

[Out]

x+6*x^2+20*x^3+40*x^4+252/5*x^5+48*x^6+352/7*x^7+48*x^8+80/3*x^9+96/5*x^10+192/1
1*x^11+64/13*x^13

_______________________________________________________________________________________

Maxima [A]  time = 0.788934, size = 77, normalized size = 1.12 \[ \frac{64}{13} \, x^{13} + \frac{192}{11} \, x^{11} + \frac{96}{5} \, x^{10} + \frac{80}{3} \, x^{9} + 48 \, x^{8} + \frac{352}{7} \, x^{7} + 48 \, x^{6} + \frac{252}{5} \, x^{5} + 40 \, x^{4} + 20 \, x^{3} + 6 \, x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

64/13*x^13 + 192/11*x^11 + 96/5*x^10 + 80/3*x^9 + 48*x^8 + 352/7*x^7 + 48*x^6 +
252/5*x^5 + 40*x^4 + 20*x^3 + 6*x^2 + x

_______________________________________________________________________________________

Fricas [A]  time = 0.227525, size = 1, normalized size = 0.01 \[ \frac{64}{13} x^{13} + \frac{192}{11} x^{11} + \frac{96}{5} x^{10} + \frac{80}{3} x^{9} + 48 x^{8} + \frac{352}{7} x^{7} + 48 x^{6} + \frac{252}{5} x^{5} + 40 x^{4} + 20 x^{3} + 6 x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

64/13*x^13 + 192/11*x^11 + 96/5*x^10 + 80/3*x^9 + 48*x^8 + 352/7*x^7 + 48*x^6 +
252/5*x^5 + 40*x^4 + 20*x^3 + 6*x^2 + x

_______________________________________________________________________________________

Sympy [A]  time = 0.093272, size = 66, normalized size = 0.96 \[ \frac{64 x^{13}}{13} + \frac{192 x^{11}}{11} + \frac{96 x^{10}}{5} + \frac{80 x^{9}}{3} + 48 x^{8} + \frac{352 x^{7}}{7} + 48 x^{6} + \frac{252 x^{5}}{5} + 40 x^{4} + 20 x^{3} + 6 x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

64*x**13/13 + 192*x**11/11 + 96*x**10/5 + 80*x**9/3 + 48*x**8 + 352*x**7/7 + 48*
x**6 + 252*x**5/5 + 40*x**4 + 20*x**3 + 6*x**2 + x

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.259721, size = 77, normalized size = 1.12 \[ \frac{64}{13} \, x^{13} + \frac{192}{11} \, x^{11} + \frac{96}{5} \, x^{10} + \frac{80}{3} \, x^{9} + 48 \, x^{8} + \frac{352}{7} \, x^{7} + 48 \, x^{6} + \frac{252}{5} \, x^{5} + 40 \, x^{4} + 20 \, x^{3} + 6 \, x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

64/13*x^13 + 192/11*x^11 + 96/5*x^10 + 80/3*x^9 + 48*x^8 + 352/7*x^7 + 48*x^6 +
252/5*x^5 + 40*x^4 + 20*x^3 + 6*x^2 + x