3.14.72 \(\int (1-2 x)^3 (2+3 x)^7 (3+5 x)^3 \, dx\) [1372]

Optimal. Leaf size=78 \[ -\frac {343 (2+3 x)^8}{17496}+\frac {1813 (2+3 x)^9}{6561}-\frac {10073 (2+3 x)^{10}}{7290}+\frac {66193 (2+3 x)^{11}}{24057}-\frac {7195 (2+3 x)^{12}}{4374}+\frac {3700 (2+3 x)^{13}}{9477}-\frac {500 (2+3 x)^{14}}{15309} \]

[Out]

-343/17496*(2+3*x)^8+1813/6561*(2+3*x)^9-10073/7290*(2+3*x)^10+66193/24057*(2+3*x)^11-7195/4374*(2+3*x)^12+370
0/9477*(2+3*x)^13-500/15309*(2+3*x)^14

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Rubi [A]
time = 0.02, antiderivative size = 78, 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)^{14}}{15309}+\frac {3700 (3 x+2)^{13}}{9477}-\frac {7195 (3 x+2)^{12}}{4374}+\frac {66193 (3 x+2)^{11}}{24057}-\frac {10073 (3 x+2)^{10}}{7290}+\frac {1813 (3 x+2)^9}{6561}-\frac {343 (3 x+2)^8}{17496} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(-343*(2 + 3*x)^8)/17496 + (1813*(2 + 3*x)^9)/6561 - (10073*(2 + 3*x)^10)/7290 + (66193*(2 + 3*x)^11)/24057 -
(7195*(2 + 3*x)^12)/4374 + (3700*(2 + 3*x)^13)/9477 - (500*(2 + 3*x)^14)/15309

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)^3 (2+3 x)^7 (3+5 x)^3 \, dx &=\int \left (-\frac {343}{729} (2+3 x)^7+\frac {1813}{243} (2+3 x)^8-\frac {10073}{243} (2+3 x)^9+\frac {66193}{729} (2+3 x)^{10}-\frac {14390}{243} (2+3 x)^{11}+\frac {3700}{243} (2+3 x)^{12}-\frac {1000}{729} (2+3 x)^{13}\right ) \, dx\\ &=-\frac {343 (2+3 x)^8}{17496}+\frac {1813 (2+3 x)^9}{6561}-\frac {10073 (2+3 x)^{10}}{7290}+\frac {66193 (2+3 x)^{11}}{24057}-\frac {7195 (2+3 x)^{12}}{4374}+\frac {3700 (2+3 x)^{13}}{9477}-\frac {500 (2+3 x)^{14}}{15309}\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 85, normalized size = 1.09 \begin {gather*} 3456 x+16416 x^2+31200 x^3-20732 x^4-\frac {1022472 x^5}{5}-299014 x^6+\frac {1241998 x^7}{7}+\frac {8511675 x^8}{8}+1119837 x^9-\frac {2909493 x^{10}}{10}-\frac {19532907 x^{11}}{11}-\frac {3595185 x^{12}}{2}-\frac {10862100 x^{13}}{13}-\frac {1093500 x^{14}}{7} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

3456*x + 16416*x^2 + 31200*x^3 - 20732*x^4 - (1022472*x^5)/5 - 299014*x^6 + (1241998*x^7)/7 + (8511675*x^8)/8
+ 1119837*x^9 - (2909493*x^10)/10 - (19532907*x^11)/11 - (3595185*x^12)/2 - (10862100*x^13)/13 - (1093500*x^14
)/7

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Maple [A]
time = 0.08, size = 70, normalized size = 0.90

method	result	size
gosper	\(-\frac {x \left (6254820000 x^{13}[phone] x^{12}[phone] x^{11}[phone] x^{10}[phone] x^{9}-44838273480 x^{8}-42600933375 x^{7}-7104228560 x^{6}[phone] x^{5}[phone] x^{4}[phone] x^{3}-1249248000 x^{2}-657296640 x -138378240\right )}{40040}\)	\(69\)
default	\(-\frac {1093500}{7} x^{14}-\frac {10862100}{13} x^{13}-\frac {3595185}{2} x^{12}-\frac {19532907}{11} x^{11}-\frac {2909493}{10} x^{10}+1119837 x^{9}+\frac {8511675}{8} x^{8}+\frac {1241998}{7} x^{7}-299014 x^{6}-\frac {1022472}{5} x^{5}-20732 x^{4}+31200 x^{3}+16416 x^{2}+3456 x\)	\(70\)
norman	\(-\frac {1093500}{7} x^{14}-\frac {10862100}{13} x^{13}-\frac {3595185}{2} x^{12}-\frac {19532907}{11} x^{11}-\frac {2909493}{10} x^{10}+1119837 x^{9}+\frac {8511675}{8} x^{8}+\frac {1241998}{7} x^{7}-299014 x^{6}-\frac {1022472}{5} x^{5}-20732 x^{4}+31200 x^{3}+16416 x^{2}+3456 x\)	\(70\)
risch	\(-\frac {1093500}{7} x^{14}-\frac {10862100}{13} x^{13}-\frac {3595185}{2} x^{12}-\frac {19532907}{11} x^{11}-\frac {2909493}{10} x^{10}+1119837 x^{9}+\frac {8511675}{8} x^{8}+\frac {1241998}{7} x^{7}-299014 x^{6}-\frac {1022472}{5} x^{5}-20732 x^{4}+31200 x^{3}+16416 x^{2}+3456 x\)	\(70\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1093500/7*x^14-10862100/13*x^13-3595185/2*x^12-19532907/11*x^11-2909493/10*x^10+1119837*x^9+8511675/8*x^8+124
1998/7*x^7-299014*x^6-1022472/5*x^5-20732*x^4+31200*x^3+16416*x^2+3456*x

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Maxima [A]
time = 0.31, size = 69, normalized size = 0.88 \begin {gather*} -\frac {1093500}{7} \, x^{14} - \frac {10862100}{13} \, x^{13} - \frac {3595185}{2} \, x^{12} - \frac {19532907}{11} \, x^{11} - \frac {2909493}{10} \, x^{10} + 1119837 \, x^{9} + \frac {8511675}{8} \, x^{8} + \frac {1241998}{7} \, x^{7} - 299014 \, x^{6} - \frac {1022472}{5} \, x^{5} - 20732 \, x^{4} + 31200 \, x^{3} + 16416 \, x^{2} + 3456 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1093500/7*x^14 - 10862100/13*x^13 - 3595185/2*x^12 - 19532907/11*x^11 - 2909493/10*x^10 + 1119837*x^9 + 85116
75/8*x^8 + 1241998/7*x^7 - 299014*x^6 - 1022472/5*x^5 - 20732*x^4 + 31200*x^3 + 16416*x^2 + 3456*x

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Fricas [A]
time = 0.42, size = 69, normalized size = 0.88 \begin {gather*} -\frac {1093500}{7} \, x^{14} - \frac {10862100}{13} \, x^{13} - \frac {3595185}{2} \, x^{12} - \frac {19532907}{11} \, x^{11} - \frac {2909493}{10} \, x^{10} + 1119837 \, x^{9} + \frac {8511675}{8} \, x^{8} + \frac {1241998}{7} \, x^{7} - 299014 \, x^{6} - \frac {1022472}{5} \, x^{5} - 20732 \, x^{4} + 31200 \, x^{3} + 16416 \, x^{2} + 3456 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1093500/7*x^14 - 10862100/13*x^13 - 3595185/2*x^12 - 19532907/11*x^11 - 2909493/10*x^10 + 1119837*x^9 + 85116
75/8*x^8 + 1241998/7*x^7 - 299014*x^6 - 1022472/5*x^5 - 20732*x^4 + 31200*x^3 + 16416*x^2 + 3456*x

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Sympy [A]
time = 0.02, size = 82, normalized size = 1.05 \begin {gather*} - \frac {1093500 x^{14}}{7} - \frac {10862100 x^{13}}{13} - \frac {3595185 x^{12}}{2} - \frac {19532907 x^{11}}{11} - \frac {2909493 x^{10}}{10} + 1119837 x^{9} + \frac {8511675 x^{8}}{8} + \frac {1241998 x^{7}}{7} - 299014 x^{6} - \frac {1022472 x^{5}}{5} - 20732 x^{4} + 31200 x^{3} + 16416 x^{2} + 3456 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1093500*x**14/7 - 10862100*x**13/13 - 3595185*x**12/2 - 19532907*x**11/11 - 2909493*x**10/10 + 1119837*x**9 +
8511675*x**8/8 + 1241998*x**7/7 - 299014*x**6 - 1022472*x**5/5 - 20732*x**4 + 31200*x**3 + 16416*x**2 + 3456*
x

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Giac [A]
time = 1.41, size = 69, normalized size = 0.88 \begin {gather*} -\frac {1093500}{7} \, x^{14} - \frac {10862100}{13} \, x^{13} - \frac {3595185}{2} \, x^{12} - \frac {19532907}{11} \, x^{11} - \frac {2909493}{10} \, x^{10} + 1119837 \, x^{9} + \frac {8511675}{8} \, x^{8} + \frac {1241998}{7} \, x^{7} - 299014 \, x^{6} - \frac {1022472}{5} \, x^{5} - 20732 \, x^{4} + 31200 \, x^{3} + 16416 \, x^{2} + 3456 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1093500/7*x^14 - 10862100/13*x^13 - 3595185/2*x^12 - 19532907/11*x^11 - 2909493/10*x^10 + 1119837*x^9 + 85116
75/8*x^8 + 1241998/7*x^7 - 299014*x^6 - 1022472/5*x^5 - 20732*x^4 + 31200*x^3 + 16416*x^2 + 3456*x

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Mupad [B]
time = 0.10, size = 69, normalized size = 0.88 \begin {gather*} -\frac {1093500\,x^{14}}{7}-\frac {10862100\,x^{13}}{13}-\frac {3595185\,x^{12}}{2}-\frac {19532907\,x^{11}}{11}-\frac {2909493\,x^{10}}{10}+1119837\,x^9+\frac {8511675\,x^8}{8}+\frac {1241998\,x^7}{7}-299014\,x^6-\frac {1022472\,x^5}{5}-20732\,x^4+31200\,x^3+16416\,x^2+3456\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3456*x + 16416*x^2 + 31200*x^3 - 20732*x^4 - (1022472*x^5)/5 - 299014*x^6 + (1241998*x^7)/7 + (8511675*x^8)/8
+ 1119837*x^9 - (2909493*x^10)/10 - (19532907*x^11)/11 - (3595185*x^12)/2 - (10862100*x^13)/13 - (1093500*x^14
)/7

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