3.1.31 \(\int (3-x+2 x^2)^3 (2+3 x+5 x^2)^3 \, dx\) [31]

Optimal. Leaf size=82 \[ 216 x+378 x^2+870 x^3+\frac {4483 x^4}{4}+\frac {8292 x^5}{5}+\frac {2873 x^6}{2}+\frac {12016 x^7}{7}+\frac {7869 x^8}{8}+\frac {3316 x^9}{3}+\frac {3061 x^{10}}{10}+\frac {4830 x^{11}}{11}+25 x^{12}+\frac {1000 x^{13}}{13} \]

[Out]

216*x+378*x^2+870*x^3+4483/4*x^4+8292/5*x^5+2873/2*x^6+12016/7*x^7+7869/8*x^8+3316/3*x^9+3061/10*x^10+4830/11*
x^11+25*x^12+1000/13*x^13

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Rubi [A]
time = 0.03, antiderivative size = 82, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {1671} \begin {gather*} \frac {1000 x^{13}}{13}+25 x^{12}+\frac {4830 x^{11}}{11}+\frac {3061 x^{10}}{10}+\frac {3316 x^9}{3}+\frac {7869 x^8}{8}+\frac {12016 x^7}{7}+\frac {2873 x^6}{2}+\frac {8292 x^5}{5}+\frac {4483 x^4}{4}+870 x^3+378 x^2+216 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

216*x + 378*x^2 + 870*x^3 + (4483*x^4)/4 + (8292*x^5)/5 + (2873*x^6)/2 + (12016*x^7)/7 + (7869*x^8)/8 + (3316*
x^9)/3 + (3061*x^10)/10 + (4830*x^11)/11 + 25*x^12 + (1000*x^13)/13

Rule 1671

Int[(Pq_)*((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[ExpandIntegrand[Pq*(a + b*x + c*x^2)^p, x
], x] /; FreeQ[{a, b, c}, x] && PolyQ[Pq, x] && IGtQ[p, -2]

Rubi steps

\begin {align*} \int \left (3-x+2 x^2\right )^3 \left (2+3 x+5 x^2\right )^3 \, dx &=\int \left (216+756 x+2610 x^2+4483 x^3+8292 x^4+8619 x^5+12016 x^6+7869 x^7+9948 x^8+3061 x^9+4830 x^{10}+300 x^{11}+1000 x^{12}\right ) \, dx\\ &=216 x+378 x^2+870 x^3+\frac {4483 x^4}{4}+\frac {8292 x^5}{5}+\frac {2873 x^6}{2}+\frac {12016 x^7}{7}+\frac {7869 x^8}{8}+\frac {3316 x^9}{3}+\frac {3061 x^{10}}{10}+\frac {4830 x^{11}}{11}+25 x^{12}+\frac {1000 x^{13}}{13}\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 82, normalized size = 1.00 \begin {gather*} 216 x+378 x^2+870 x^3+\frac {4483 x^4}{4}+\frac {8292 x^5}{5}+\frac {2873 x^6}{2}+\frac {12016 x^7}{7}+\frac {7869 x^8}{8}+\frac {3316 x^9}{3}+\frac {3061 x^{10}}{10}+\frac {4830 x^{11}}{11}+25 x^{12}+\frac {1000 x^{13}}{13} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

216*x + 378*x^2 + 870*x^3 + (4483*x^4)/4 + (8292*x^5)/5 + (2873*x^6)/2 + (12016*x^7)/7 + (7869*x^8)/8 + (3316*
x^9)/3 + (3061*x^10)/10 + (4830*x^11)/11 + 25*x^12 + (1000*x^13)/13

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Maple [A]
time = 0.11, size = 65, normalized size = 0.79

method	result	size
gosper	\(216 x +378 x^{2}+870 x^{3}+\frac {4483}{4} x^{4}+\frac {8292}{5} x^{5}+\frac {2873}{2} x^{6}+\frac {12016}{7} x^{7}+\frac {7869}{8} x^{8}+\frac {3316}{3} x^{9}+\frac {3061}{10} x^{10}+\frac {4830}{11} x^{11}+25 x^{12}+\frac {1000}{13} x^{13}\)	\(65\)
default	\(216 x +378 x^{2}+870 x^{3}+\frac {4483}{4} x^{4}+\frac {8292}{5} x^{5}+\frac {2873}{2} x^{6}+\frac {12016}{7} x^{7}+\frac {7869}{8} x^{8}+\frac {3316}{3} x^{9}+\frac {3061}{10} x^{10}+\frac {4830}{11} x^{11}+25 x^{12}+\frac {1000}{13} x^{13}\)	\(65\)
norman	\(216 x +378 x^{2}+870 x^{3}+\frac {4483}{4} x^{4}+\frac {8292}{5} x^{5}+\frac {2873}{2} x^{6}+\frac {12016}{7} x^{7}+\frac {7869}{8} x^{8}+\frac {3316}{3} x^{9}+\frac {3061}{10} x^{10}+\frac {4830}{11} x^{11}+25 x^{12}+\frac {1000}{13} x^{13}\)	\(65\)
risch	\(216 x +378 x^{2}+870 x^{3}+\frac {4483}{4} x^{4}+\frac {8292}{5} x^{5}+\frac {2873}{2} x^{6}+\frac {12016}{7} x^{7}+\frac {7869}{8} x^{8}+\frac {3316}{3} x^{9}+\frac {3061}{10} x^{10}+\frac {4830}{11} x^{11}+25 x^{12}+\frac {1000}{13} x^{13}\)	\(65\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x^2-x+3)^3*(5*x^2+3*x+2)^3,x,method=_RETURNVERBOSE)

[Out]

216*x+378*x^2+870*x^3+4483/4*x^4+8292/5*x^5+2873/2*x^6+12016/7*x^7+7869/8*x^8+3316/3*x^9+3061/10*x^10+4830/11*
x^11+25*x^12+1000/13*x^13

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Maxima [A]
time = 0.28, size = 64, normalized size = 0.78 \begin {gather*} \frac {1000}{13} \, x^{13} + 25 \, x^{12} + \frac {4830}{11} \, x^{11} + \frac {3061}{10} \, x^{10} + \frac {3316}{3} \, x^{9} + \frac {7869}{8} \, x^{8} + \frac {12016}{7} \, x^{7} + \frac {2873}{2} \, x^{6} + \frac {8292}{5} \, x^{5} + \frac {4483}{4} \, x^{4} + 870 \, x^{3} + 378 \, x^{2} + 216 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1000/13*x^13 + 25*x^12 + 4830/11*x^11 + 3061/10*x^10 + 3316/3*x^9 + 7869/8*x^8 + 12016/7*x^7 + 2873/2*x^6 + 82
92/5*x^5 + 4483/4*x^4 + 870*x^3 + 378*x^2 + 216*x

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Fricas [A]
time = 2.25, size = 64, normalized size = 0.78 \begin {gather*} \frac {1000}{13} \, x^{13} + 25 \, x^{12} + \frac {4830}{11} \, x^{11} + \frac {3061}{10} \, x^{10} + \frac {3316}{3} \, x^{9} + \frac {7869}{8} \, x^{8} + \frac {12016}{7} \, x^{7} + \frac {2873}{2} \, x^{6} + \frac {8292}{5} \, x^{5} + \frac {4483}{4} \, x^{4} + 870 \, x^{3} + 378 \, x^{2} + 216 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1000/13*x^13 + 25*x^12 + 4830/11*x^11 + 3061/10*x^10 + 3316/3*x^9 + 7869/8*x^8 + 12016/7*x^7 + 2873/2*x^6 + 82
92/5*x^5 + 4483/4*x^4 + 870*x^3 + 378*x^2 + 216*x

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Sympy [A]
time = 0.02, size = 78, normalized size = 0.95 \begin {gather*} \frac {1000 x^{13}}{13} + 25 x^{12} + \frac {4830 x^{11}}{11} + \frac {3061 x^{10}}{10} + \frac {3316 x^{9}}{3} + \frac {7869 x^{8}}{8} + \frac {12016 x^{7}}{7} + \frac {2873 x^{6}}{2} + \frac {8292 x^{5}}{5} + \frac {4483 x^{4}}{4} + 870 x^{3} + 378 x^{2} + 216 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x**2-x+3)**3*(5*x**2+3*x+2)**3,x)

[Out]

1000*x**13/13 + 25*x**12 + 4830*x**11/11 + 3061*x**10/10 + 3316*x**9/3 + 7869*x**8/8 + 12016*x**7/7 + 2873*x**
6/2 + 8292*x**5/5 + 4483*x**4/4 + 870*x**3 + 378*x**2 + 216*x

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Giac [A]
time = 4.37, size = 64, normalized size = 0.78 \begin {gather*} \frac {1000}{13} \, x^{13} + 25 \, x^{12} + \frac {4830}{11} \, x^{11} + \frac {3061}{10} \, x^{10} + \frac {3316}{3} \, x^{9} + \frac {7869}{8} \, x^{8} + \frac {12016}{7} \, x^{7} + \frac {2873}{2} \, x^{6} + \frac {8292}{5} \, x^{5} + \frac {4483}{4} \, x^{4} + 870 \, x^{3} + 378 \, x^{2} + 216 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1000/13*x^13 + 25*x^12 + 4830/11*x^11 + 3061/10*x^10 + 3316/3*x^9 + 7869/8*x^8 + 12016/7*x^7 + 2873/2*x^6 + 82
92/5*x^5 + 4483/4*x^4 + 870*x^3 + 378*x^2 + 216*x

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Mupad [B]
time = 0.08, size = 64, normalized size = 0.78 \begin {gather*} \frac {1000\,x^{13}}{13}+25\,x^{12}+\frac {4830\,x^{11}}{11}+\frac {3061\,x^{10}}{10}+\frac {3316\,x^9}{3}+\frac {7869\,x^8}{8}+\frac {12016\,x^7}{7}+\frac {2873\,x^6}{2}+\frac {8292\,x^5}{5}+\frac {4483\,x^4}{4}+870\,x^3+378\,x^2+216\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x^2 - x + 3)^3*(3*x + 5*x^2 + 2)^3,x)

[Out]

216*x + 378*x^2 + 870*x^3 + (4483*x^4)/4 + (8292*x^5)/5 + (2873*x^6)/2 + (12016*x^7)/7 + (7869*x^8)/8 + (3316*
x^9)/3 + (3061*x^10)/10 + (4830*x^11)/11 + 25*x^12 + (1000*x^13)/13

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