3.663 \(\int (2+3 x)^6 \left (1+(2+3 x)^7+(2+3 x)^{14}\right ) \, dx\)

Optimal. Leaf size=34 \[ \frac{1}{63} (3 x+2)^{21}+\frac{1}{42} (3 x+2)^{14}+\frac{1}{21} (3 x+2)^7 \]

[Out]

(2 + 3*x)^7/21 + (2 + 3*x)^14/42 + (2 + 3*x)^21/63

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Rubi [A]  time = 0.0797298, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ \frac{1}{63} (3 x+2)^{21}+\frac{1}{42} (3 x+2)^{14}+\frac{1}{21} (3 x+2)^7 \]

Antiderivative was successfully verified.

[In]  Int[(2 + 3*x)^6*(1 + (2 + 3*x)^7 + (2 + 3*x)^14),x]

[Out]

(2 + 3*x)^7/21 + (2 + 3*x)^14/42 + (2 + 3*x)^21/63

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{\left (3 x + 2\right )^{21}}{63} + \frac{\left (3 x + 2\right )^{7}}{21} + \frac{\int ^{\left (3 x + 2\right )^{7}} x\, dx}{21} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**6*(1+(2+3*x)**7+(2+3*x)**14),x)

[Out]

(3*x + 2)**21/63 + (3*x + 2)**7/21 + Integral(x, (x, (3*x + 2)**7))/21

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Mathematica [A]  time = 0.0139212, size = 34, normalized size = 1. \[ \frac{1}{63} (3 x+2)^{21}+\frac{1}{42} (3 x+2)^{14}+\frac{1}{21} (3 x+2)^7 \]

Antiderivative was successfully verified.

[In]  Integrate[(2 + 3*x)^6*(1 + (2 + 3*x)^7 + (2 + 3*x)^14),x]

[Out]

(2 + 3*x)^7/21 + (2 + 3*x)^14/42 + (2 + 3*x)^21/63

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Maple [B]  time = 0.003, size = 105, normalized size = 3.1 \[{\frac{1162261467\,{x}^{21}}{7}}[phone]\,{x}^{20}[phone]\,{x}^{19}[phone]\,{x}^{18}[phone]\,{x}^{17}[phone]\,{x}^{16}[phone]\,{x}^{15}+{\frac{15819767221203\,{x}^{14}}{14}}[phone]\,{x}^{13}[phone]\,{x}^{12}[phone]\,{x}^{11}[phone]\,{x}^{10}[phone]\,{x}^{9}[phone]\,{x}^{8}[phone]\,{x}^{7}[phone]\,{x}^{6}[phone]\,{x}^{5}[phone]\,{x}^{4}[phone]\,{x}^{3}[phone]\,{x}^{2}+1056832\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^6*(1+(2+3*x)^7+(2+3*x)^14),x)

[Out]

1162261467/7*x^21+2324522934*x^20+15496819560*x^19+65431015920*x^18+196293047760
*x^17+444930908256*x^16+790988281344*x^15+15819767221203/14*x^14+1318314865122*x
^13+1269491970942*x^12+1015602174288*x^11+677082445416*x^10+376174427616*x^9+173
635132896*x^8+66158154783*x^7+20588764518*x^6+5149786572*x^5+1010576952*x^4+1499
02032*x^3+15808800*x^2+1056832*x

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Maxima [A]  time = 0.782857, size = 140, normalized size = 4.12 \[ \frac{1162261467}{7} \, x^{21} + 2324522934 \, x^{20} + 15496819560 \, x^{19} + 65431015920 \, x^{18} + 196293047760 \, x^{17} + 444930908256 \, x^{16} + 790988281344 \, x^{15} + \frac{15819767221203}{14} \, x^{14} + 1318314865122 \, x^{13} + 1269491970942 \, x^{12} + 1015602174288 \, x^{11} + 677082445416 \, x^{10} + 376174427616 \, x^{9} + 173635132896 \, x^{8} + 66158154783 \, x^{7} + 20588764518 \, x^{6} + 5149786572 \, x^{5} + 1010576952 \, x^{4} + 149902032 \, x^{3} + 15808800 \, x^{2} + 1056832 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(((3*x + 2)^14 + (3*x + 2)^7 + 1)*(3*x + 2)^6,x, algorithm="maxima")

[Out]

1162261467/7*x^21 + 2324522934*x^20 + 15496819560*x^19 + 65431015920*x^18 + 1962
93047760*x^17 + 444930908256*x^16 + 790988281344*x^15 + 15819767221203/14*x^14 +
1318314865122*x^13 + 1269491970942*x^12 + 1015602174288*x^11 + 677082445416*x^1
0 + 376174427616*x^9 + 173635132896*x^8 + 66158154783*x^7 + 20588764518*x^6 + 51
49786572*x^5 + 1010576952*x^4 + 149902032*x^3 + 15808800*x^2 + 1056832*x

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Fricas [A]  time = 0.244678, size = 1, normalized size = 0.03 \[ \frac{1162261467}{7} x^{21} + 2324522934 x^{20} + 15496819560 x^{19} + 65431015920 x^{18} + 196293047760 x^{17} + 444930908256 x^{16} + 790988281344 x^{15} + \frac{15819767221203}{14} x^{14} + 1318314865122 x^{13} + 1269491970942 x^{12} + 1015602174288 x^{11} + 677082445416 x^{10} + 376174427616 x^{9} + 173635132896 x^{8} + 66158154783 x^{7} + 20588764518 x^{6} + 5149786572 x^{5} + 1010576952 x^{4} + 149902032 x^{3} + 15808800 x^{2} + 1056832 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(((3*x + 2)^14 + (3*x + 2)^7 + 1)*(3*x + 2)^6,x, algorithm="fricas")

[Out]

1162261467/7*x^21 + 2324522934*x^20 + 15496819560*x^19 + 65431015920*x^18 + 1962
93047760*x^17 + 444930908256*x^16 + 790988281344*x^15 + 15819767221203/14*x^14 +
1318314865122*x^13 + 1269491970942*x^12 + 1015602174288*x^11 + 677082445416*x^1
0 + 376174427616*x^9 + 173635132896*x^8 + 66158154783*x^7 + 20588764518*x^6 + 51
49786572*x^5 + 1010576952*x^4 + 149902032*x^3 + 15808800*x^2 + 1056832*x

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Sympy [A]  time = 0.176918, size = 107, normalized size = 3.15 \[ \frac{1162261467 x^{21}}{7} + 2324522934 x^{20} + 15496819560 x^{19} + 65431015920 x^{18} + 196293047760 x^{17} + 444930908256 x^{16} + 790988281344 x^{15} + \frac{15819767221203 x^{14}}{14} + 1318314865122 x^{13} + 1269491970942 x^{12} + 1015602174288 x^{11} + 677082445416 x^{10} + 376174427616 x^{9} + 173635132896 x^{8} + 66158154783 x^{7} + 20588764518 x^{6} + 5149786572 x^{5} + 1010576952 x^{4} + 149902032 x^{3} + 15808800 x^{2} + 1056832 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**6*(1+(2+3*x)**7+(2+3*x)**14),x)

[Out]

1162261467*x**21/7 + 2324522934*x**20 + 15496819560*x**19 + 65431015920*x**18 +
196293047760*x**17 + 444930908256*x**16 + 790988281344*x**15 + 15819767221203*x*
*14/14 + 1318314865122*x**13 + 1269491970942*x**12 + 1015602174288*x**11 + 67708
2445416*x**10 + 376174427616*x**9 + 173635132896*x**8 + 66158154783*x**7 + 20588
764518*x**6 + 5149786572*x**5 + 1010576952*x**4 + 149902032*x**3 + 15808800*x**2
+ 1056832*x

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GIAC/XCAS [A]  time = 0.27301, size = 38, normalized size = 1.12 \[ \frac{1}{63} \,{\left (3 \, x + 2\right )}^{21} + \frac{1}{42} \,{\left (3 \, x + 2\right )}^{14} + \frac{1}{21} \,{\left (3 \, x + 2\right )}^{7} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(((3*x + 2)^14 + (3*x + 2)^7 + 1)*(3*x + 2)^6,x, algorithm="giac")

[Out]

1/63*(3*x + 2)^21 + 1/42*(3*x + 2)^14 + 1/21*(3*x + 2)^7