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

Optimal. Leaf size=96 \[ \frac{1000 x^{15}}{3}+\frac{2250 x^{14}}{7}+\frac{27050 x^{13}}{13}+\frac{30395 x^{12}}{12}+\frac{68583 x^{11}}{11}+\frac{75311 x^{10}}{10}+\frac{103583 x^9}{9}+\frac{94881 x^8}{8}+\frac{91349 x^7}{7}+\frac{64529 x^6}{6}+\frac{43083 x^5}{5}+5144 x^4+2856 x^3+1080 x^2+432 x \]

[Out]

432*x + 1080*x^2 + 2856*x^3 + 5144*x^4 + (43083*x^5)/5 + (64529*x^6)/6 + (91349*x^7)/7 + (94881*x^8)/8 + (1035
83*x^9)/9 + (75311*x^10)/10 + (68583*x^11)/11 + (30395*x^12)/12 + (27050*x^13)/13 + (2250*x^14)/7 + (1000*x^15
)/3

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Rubi [A]  time = 0.0705267, antiderivative size = 96, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.04, Rules used = {1657} \[ \frac{1000 x^{15}}{3}+\frac{2250 x^{14}}{7}+\frac{27050 x^{13}}{13}+\frac{30395 x^{12}}{12}+\frac{68583 x^{11}}{11}+\frac{75311 x^{10}}{10}+\frac{103583 x^9}{9}+\frac{94881 x^8}{8}+\frac{91349 x^7}{7}+\frac{64529 x^6}{6}+\frac{43083 x^5}{5}+5144 x^4+2856 x^3+1080 x^2+432 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

432*x + 1080*x^2 + 2856*x^3 + 5144*x^4 + (43083*x^5)/5 + (64529*x^6)/6 + (91349*x^7)/7 + (94881*x^8)/8 + (1035
83*x^9)/9 + (75311*x^10)/10 + (68583*x^11)/11 + (30395*x^12)/12 + (27050*x^13)/13 + (2250*x^14)/7 + (1000*x^15
)/3

Rule 1657

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 )^4 \, dx &=\int \left (432+2160 x+8568 x^2+20576 x^3+43083 x^4+64529 x^5+91349 x^6+94881 x^7+103583 x^8+75311 x^9+68583 x^{10}+30395 x^{11}+27050 x^{12}+4500 x^{13}+5000 x^{14}\right ) \, dx\\ &=432 x+1080 x^2+2856 x^3+5144 x^4+\frac{43083 x^5}{5}+\frac{64529 x^6}{6}+\frac{91349 x^7}{7}+\frac{94881 x^8}{8}+\frac{103583 x^9}{9}+\frac{75311 x^{10}}{10}+\frac{68583 x^{11}}{11}+\frac{30395 x^{12}}{12}+\frac{27050 x^{13}}{13}+\frac{2250 x^{14}}{7}+\frac{1000 x^{15}}{3}\\ \end{align*}

Mathematica [A]  time = 0.0029899, size = 96, normalized size = 1. \[ \frac{1000 x^{15}}{3}+\frac{2250 x^{14}}{7}+\frac{27050 x^{13}}{13}+\frac{30395 x^{12}}{12}+\frac{68583 x^{11}}{11}+\frac{75311 x^{10}}{10}+\frac{103583 x^9}{9}+\frac{94881 x^8}{8}+\frac{91349 x^7}{7}+\frac{64529 x^6}{6}+\frac{43083 x^5}{5}+5144 x^4+2856 x^3+1080 x^2+432 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

432*x + 1080*x^2 + 2856*x^3 + 5144*x^4 + (43083*x^5)/5 + (64529*x^6)/6 + (91349*x^7)/7 + (94881*x^8)/8 + (1035
83*x^9)/9 + (75311*x^10)/10 + (68583*x^11)/11 + (30395*x^12)/12 + (27050*x^13)/13 + (2250*x^14)/7 + (1000*x^15
)/3

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Maple [A]  time = 0.044, size = 75, normalized size = 0.8 \begin{align*} 432\,x+1080\,{x}^{2}+2856\,{x}^{3}+5144\,{x}^{4}+{\frac{43083\,{x}^{5}}{5}}+{\frac{64529\,{x}^{6}}{6}}+{\frac{91349\,{x}^{7}}{7}}+{\frac{94881\,{x}^{8}}{8}}+{\frac{103583\,{x}^{9}}{9}}+{\frac{75311\,{x}^{10}}{10}}+{\frac{68583\,{x}^{11}}{11}}+{\frac{30395\,{x}^{12}}{12}}+{\frac{27050\,{x}^{13}}{13}}+{\frac{2250\,{x}^{14}}{7}}+{\frac{1000\,{x}^{15}}{3}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x^2-x+3)^3*(5*x^2+3*x+2)^4,x)

[Out]

432*x+1080*x^2+2856*x^3+5144*x^4+43083/5*x^5+64529/6*x^6+91349/7*x^7+94881/8*x^8+103583/9*x^9+75311/10*x^10+68
583/11*x^11+30395/12*x^12+27050/13*x^13+2250/7*x^14+1000/3*x^15

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Maxima [A]  time = 0.983455, size = 100, normalized size = 1.04 \begin{align*} \frac{1000}{3} \, x^{15} + \frac{2250}{7} \, x^{14} + \frac{27050}{13} \, x^{13} + \frac{30395}{12} \, x^{12} + \frac{68583}{11} \, x^{11} + \frac{75311}{10} \, x^{10} + \frac{103583}{9} \, x^{9} + \frac{94881}{8} \, x^{8} + \frac{91349}{7} \, x^{7} + \frac{64529}{6} \, x^{6} + \frac{43083}{5} \, x^{5} + 5144 \, x^{4} + 2856 \, x^{3} + 1080 \, x^{2} + 432 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1000/3*x^15 + 2250/7*x^14 + 27050/13*x^13 + 30395/12*x^12 + 68583/11*x^11 + 75311/10*x^10 + 103583/9*x^9 + 948
81/8*x^8 + 91349/7*x^7 + 64529/6*x^6 + 43083/5*x^5 + 5144*x^4 + 2856*x^3 + 1080*x^2 + 432*x

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Fricas [A]  time = 0.823481, size = 274, normalized size = 2.85 \begin{align*} \frac{1000}{3} x^{15} + \frac{2250}{7} x^{14} + \frac{27050}{13} x^{13} + \frac{30395}{12} x^{12} + \frac{68583}{11} x^{11} + \frac{75311}{10} x^{10} + \frac{103583}{9} x^{9} + \frac{94881}{8} x^{8} + \frac{91349}{7} x^{7} + \frac{64529}{6} x^{6} + \frac{43083}{5} x^{5} + 5144 x^{4} + 2856 x^{3} + 1080 x^{2} + 432 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1000/3*x^15 + 2250/7*x^14 + 27050/13*x^13 + 30395/12*x^12 + 68583/11*x^11 + 75311/10*x^10 + 103583/9*x^9 + 948
81/8*x^8 + 91349/7*x^7 + 64529/6*x^6 + 43083/5*x^5 + 5144*x^4 + 2856*x^3 + 1080*x^2 + 432*x

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Sympy [A]  time = 0.126187, size = 92, normalized size = 0.96 \begin{align*} \frac{1000 x^{15}}{3} + \frac{2250 x^{14}}{7} + \frac{27050 x^{13}}{13} + \frac{30395 x^{12}}{12} + \frac{68583 x^{11}}{11} + \frac{75311 x^{10}}{10} + \frac{103583 x^{9}}{9} + \frac{94881 x^{8}}{8} + \frac{91349 x^{7}}{7} + \frac{64529 x^{6}}{6} + \frac{43083 x^{5}}{5} + 5144 x^{4} + 2856 x^{3} + 1080 x^{2} + 432 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x**2-x+3)**3*(5*x**2+3*x+2)**4,x)

[Out]

1000*x**15/3 + 2250*x**14/7 + 27050*x**13/13 + 30395*x**12/12 + 68583*x**11/11 + 75311*x**10/10 + 103583*x**9/
9 + 94881*x**8/8 + 91349*x**7/7 + 64529*x**6/6 + 43083*x**5/5 + 5144*x**4 + 2856*x**3 + 1080*x**2 + 432*x

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Giac [A]  time = 1.17693, size = 100, normalized size = 1.04 \begin{align*} \frac{1000}{3} \, x^{15} + \frac{2250}{7} \, x^{14} + \frac{27050}{13} \, x^{13} + \frac{30395}{12} \, x^{12} + \frac{68583}{11} \, x^{11} + \frac{75311}{10} \, x^{10} + \frac{103583}{9} \, x^{9} + \frac{94881}{8} \, x^{8} + \frac{91349}{7} \, x^{7} + \frac{64529}{6} \, x^{6} + \frac{43083}{5} \, x^{5} + 5144 \, x^{4} + 2856 \, x^{3} + 1080 \, x^{2} + 432 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1000/3*x^15 + 2250/7*x^14 + 27050/13*x^13 + 30395/12*x^12 + 68583/11*x^11 + 75311/10*x^10 + 103583/9*x^9 + 948
81/8*x^8 + 91349/7*x^7 + 64529/6*x^6 + 43083/5*x^5 + 5144*x^4 + 2856*x^3 + 1080*x^2 + 432*x