3.13.73 \(\int (1-2 x)^2 (2+3 x)^7 (3+5 x)^3 \, dx\) [1273]

Optimal. Leaf size=67 \[ -\frac {49 (2+3 x)^8}{5832}+\frac {763 (2+3 x)^9}{6561}-\frac {4099 (2+3 x)^{10}}{7290}+\frac {8285 (2+3 x)^{11}}{8019}-\frac {950 (2+3 x)^{12}}{2187}+\frac {500 (2+3 x)^{13}}{9477} \]

[Out]

-49/5832*(2+3*x)^8+763/6561*(2+3*x)^9-4099/7290*(2+3*x)^10+8285/8019*(2+3*x)^11-950/2187*(2+3*x)^12+500/9477*(
2+3*x)^13

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Rubi [A]
time = 0.02, antiderivative size = 67, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \begin {gather*} \frac {500 (3 x+2)^{13}}{9477}-\frac {950 (3 x+2)^{12}}{2187}+\frac {8285 (3 x+2)^{11}}{8019}-\frac {4099 (3 x+2)^{10}}{7290}+\frac {763 (3 x+2)^9}{6561}-\frac {49 (3 x+2)^8}{5832} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x)^3,x]

[Out]

(-49*(2 + 3*x)^8)/5832 + (763*(2 + 3*x)^9)/6561 - (4099*(2 + 3*x)^10)/7290 + (8285*(2 + 3*x)^11)/8019 - (950*(
2 + 3*x)^12)/2187 + (500*(2 + 3*x)^13)/9477

Rule 90

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandI
ntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] &&
(IntegerQ[p] || (GtQ[m, 0] && GeQ[n, -1]))

Rubi steps

\begin {align*} \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^3 \, dx &=\int \left (-\frac {49}{243} (2+3 x)^7+\frac {763}{243} (2+3 x)^8-\frac {4099}{243} (2+3 x)^9+\frac {8285}{243} (2+3 x)^{10}-\frac {3800}{243} (2+3 x)^{11}+\frac {500}{243} (2+3 x)^{12}\right ) \, dx\\ &=-\frac {49 (2+3 x)^8}{5832}+\frac {763 (2+3 x)^9}{6561}-\frac {4099 (2+3 x)^{10}}{7290}+\frac {8285 (2+3 x)^{11}}{8019}-\frac {950 (2+3 x)^{12}}{2187}+\frac {500 (2+3 x)^{13}}{9477}\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 76, normalized size = 1.13 \begin {gather*} 3456 x+19872 x^2+57696 x^3+65812 x^4-\frac {495976 x^5}{5}-\frac {1393018 x^6}{3}-618582 x^7-\frac {148473 x^8}{8}+1086843 x^9+\frac {16653681 x^{10}}{10}+\frac {13774455 x^{11}}{11}+498150 x^{12}+\frac {1093500 x^{13}}{13} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x)^3,x]

[Out]

3456*x + 19872*x^2 + 57696*x^3 + 65812*x^4 - (495976*x^5)/5 - (1393018*x^6)/3 - 618582*x^7 - (148473*x^8)/8 +
1086843*x^9 + (16653681*x^10)/10 + (13774455*x^11)/11 + 498150*x^12 + (1093500*x^13)/13

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Maple [A]
time = 0.08, size = 65, normalized size = 0.97

method	result	size
gosper	\(\frac {x \left (1443420000 x^{12}[phone] x^{11}[phone] x^{10}[phone] x^{9}[phone] x^{8}-318474585 x^{7}-10614867120 x^{6}-7968062960 x^{5}-1702189632 x^{4}[phone] x^{3}[phone] x^{2}[phone] x [phone]\right )}{17160}\)	\(64\)
default	\(\frac {1093500}{13} x^{13}+498150 x^{12}+\frac {13774455}{11} x^{11}+\frac {16653681}{10} x^{10}+1086843 x^{9}-\frac {148473}{8} x^{8}-618582 x^{7}-\frac {1393018}{3} x^{6}-\frac {495976}{5} x^{5}+65812 x^{4}+57696 x^{3}+19872 x^{2}+3456 x\)	\(65\)
norman	\(\frac {1093500}{13} x^{13}+498150 x^{12}+\frac {13774455}{11} x^{11}+\frac {16653681}{10} x^{10}+1086843 x^{9}-\frac {148473}{8} x^{8}-618582 x^{7}-\frac {1393018}{3} x^{6}-\frac {495976}{5} x^{5}+65812 x^{4}+57696 x^{3}+19872 x^{2}+3456 x\)	\(65\)
risch	\(\frac {1093500}{13} x^{13}+498150 x^{12}+\frac {13774455}{11} x^{11}+\frac {16653681}{10} x^{10}+1086843 x^{9}-\frac {148473}{8} x^{8}-618582 x^{7}-\frac {1393018}{3} x^{6}-\frac {495976}{5} x^{5}+65812 x^{4}+57696 x^{3}+19872 x^{2}+3456 x\)	\(65\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^2*(2+3*x)^7*(3+5*x)^3,x,method=_RETURNVERBOSE)

[Out]

1093500/13*x^13+498150*x^12+13774455/11*x^11+16653681/10*x^10+1086843*x^9-148473/8*x^8-618582*x^7-1393018/3*x^
6-495976/5*x^5+65812*x^4+57696*x^3+19872*x^2+3456*x

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Maxima [A]
time = 0.31, size = 64, normalized size = 0.96 \begin {gather*} \frac {1093500}{13} \, x^{13} + 498150 \, x^{12} + \frac {13774455}{11} \, x^{11} + \frac {16653681}{10} \, x^{10} + 1086843 \, x^{9} - \frac {148473}{8} \, x^{8} - 618582 \, x^{7} - \frac {1393018}{3} \, x^{6} - \frac {495976}{5} \, x^{5} + 65812 \, x^{4} + 57696 \, x^{3} + 19872 \, x^{2} + 3456 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^7*(3+5*x)^3,x, algorithm="maxima")

[Out]

1093500/13*x^13 + 498150*x^12 + 13774455/11*x^11 + 16653681/10*x^10 + 1086843*x^9 - 148473/8*x^8 - 618582*x^7
- 1393018/3*x^6 - 495976/5*x^5 + 65812*x^4 + 57696*x^3 + 19872*x^2 + 3456*x

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Fricas [A]
time = 0.39, size = 64, normalized size = 0.96 \begin {gather*} \frac {1093500}{13} \, x^{13} + 498150 \, x^{12} + \frac {13774455}{11} \, x^{11} + \frac {16653681}{10} \, x^{10} + 1086843 \, x^{9} - \frac {148473}{8} \, x^{8} - 618582 \, x^{7} - \frac {1393018}{3} \, x^{6} - \frac {495976}{5} \, x^{5} + 65812 \, x^{4} + 57696 \, x^{3} + 19872 \, x^{2} + 3456 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^7*(3+5*x)^3,x, algorithm="fricas")

[Out]

1093500/13*x^13 + 498150*x^12 + 13774455/11*x^11 + 16653681/10*x^10 + 1086843*x^9 - 148473/8*x^8 - 618582*x^7
- 1393018/3*x^6 - 495976/5*x^5 + 65812*x^4 + 57696*x^3 + 19872*x^2 + 3456*x

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Sympy [A]
time = 0.02, size = 73, normalized size = 1.09 \begin {gather*} \frac {1093500 x^{13}}{13} + 498150 x^{12} + \frac {13774455 x^{11}}{11} + \frac {16653681 x^{10}}{10} + 1086843 x^{9} - \frac {148473 x^{8}}{8} - 618582 x^{7} - \frac {1393018 x^{6}}{3} - \frac {495976 x^{5}}{5} + 65812 x^{4} + 57696 x^{3} + 19872 x^{2} + 3456 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**2*(2+3*x)**7*(3+5*x)**3,x)

[Out]

1093500*x**13/13 + 498150*x**12 + 13774455*x**11/11 + 16653681*x**10/10 + 1086843*x**9 - 148473*x**8/8 - 61858
2*x**7 - 1393018*x**6/3 - 495976*x**5/5 + 65812*x**4 + 57696*x**3 + 19872*x**2 + 3456*x

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Giac [A]
time = 1.70, size = 64, normalized size = 0.96 \begin {gather*} \frac {1093500}{13} \, x^{13} + 498150 \, x^{12} + \frac {13774455}{11} \, x^{11} + \frac {16653681}{10} \, x^{10} + 1086843 \, x^{9} - \frac {148473}{8} \, x^{8} - 618582 \, x^{7} - \frac {1393018}{3} \, x^{6} - \frac {495976}{5} \, x^{5} + 65812 \, x^{4} + 57696 \, x^{3} + 19872 \, x^{2} + 3456 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^7*(3+5*x)^3,x, algorithm="giac")

[Out]

1093500/13*x^13 + 498150*x^12 + 13774455/11*x^11 + 16653681/10*x^10 + 1086843*x^9 - 148473/8*x^8 - 618582*x^7
- 1393018/3*x^6 - 495976/5*x^5 + 65812*x^4 + 57696*x^3 + 19872*x^2 + 3456*x

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Mupad [B]
time = 0.08, size = 64, normalized size = 0.96 \begin {gather*} \frac {1093500\,x^{13}}{13}+498150\,x^{12}+\frac {13774455\,x^{11}}{11}+\frac {16653681\,x^{10}}{10}+1086843\,x^9-\frac {148473\,x^8}{8}-618582\,x^7-\frac {1393018\,x^6}{3}-\frac {495976\,x^5}{5}+65812\,x^4+57696\,x^3+19872\,x^2+3456\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x - 1)^2*(3*x + 2)^7*(5*x + 3)^3,x)

[Out]

3456*x + 19872*x^2 + 57696*x^3 + 65812*x^4 - (495976*x^5)/5 - (1393018*x^6)/3 - 618582*x^7 - (148473*x^8)/8 +
1086843*x^9 + (16653681*x^10)/10 + (13774455*x^11)/11 + 498150*x^12 + (1093500*x^13)/13

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