3.12.15 \(\int (1-2 x)^2 (2+3 x)^7 (3+5 x)^2 \, dx\)

Optimal. Leaf size=56 \[ \frac {25}{729} (3 x+2)^{12}-\frac {740 (3 x+2)^{11}}{2673}+\frac {503}{810} (3 x+2)^{10}-\frac {518 (3 x+2)^9}{2187}+\frac {49 (3 x+2)^8}{1944} \]

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Rubi [A]  time = 0.03, antiderivative size = 56, 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 = {88} \begin {gather*} \frac {25}{729} (3 x+2)^{12}-\frac {740 (3 x+2)^{11}}{2673}+\frac {503}{810} (3 x+2)^{10}-\frac {518 (3 x+2)^9}{2187}+\frac {49 (3 x+2)^8}{1944} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(49*(2 + 3*x)^8)/1944 - (518*(2 + 3*x)^9)/2187 + (503*(2 + 3*x)^10)/810 - (740*(2 + 3*x)^11)/2673 + (25*(2 + 3
*x)^12)/729

Rule 88

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)^2 \, dx &=\int \left (\frac {49}{81} (2+3 x)^7-\frac {518}{81} (2+3 x)^8+\frac {503}{27} (2+3 x)^9-\frac {740}{81} (2+3 x)^{10}+\frac {100}{81} (2+3 x)^{11}\right ) \, dx\\ &=\frac {49 (2+3 x)^8}{1944}-\frac {518 (2+3 x)^9}{2187}+\frac {503}{810} (2+3 x)^{10}-\frac {740 (2+3 x)^{11}}{2673}+\frac {25}{729} (2+3 x)^{12}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 69, normalized size = 1.23 \begin {gather*} 18225 x^{12}+\frac {1064340 x^{11}}{11}+\frac {2116287 x^{10}}{10}+228996 x^9+\frac {719739 x^8}{8}-65934 x^7-98182 x^6-\frac {203752 x^5}{5}+5764 x^4+\frac {38816 x^3}{3}+5664 x^2+1152 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

1152*x + 5664*x^2 + (38816*x^3)/3 + 5764*x^4 - (203752*x^5)/5 - 98182*x^6 - 65934*x^7 + (719739*x^8)/8 + 22899
6*x^9 + (2116287*x^10)/10 + (1064340*x^11)/11 + 18225*x^12

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^2 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.22, size = 59, normalized size = 1.05 \begin {gather*} 18225 x^{12} + \frac {1064340}{11} x^{11} + \frac {2116287}{10} x^{10} + 228996 x^{9} + \frac {719739}{8} x^{8} - 65934 x^{7} - 98182 x^{6} - \frac {203752}{5} x^{5} + 5764 x^{4} + \frac {38816}{3} x^{3} + 5664 x^{2} + 1152 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)^2,x, algorithm="fricas")

[Out]

18225*x^12 + 1064340/11*x^11 + 2116287/10*x^10 + 228996*x^9 + 719739/8*x^8 - 65934*x^7 - 98182*x^6 - 203752/5*
x^5 + 5764*x^4 + 38816/3*x^3 + 5664*x^2 + 1152*x

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giac [A]  time = 1.14, size = 59, normalized size = 1.05 \begin {gather*} 18225 \, x^{12} + \frac {1064340}{11} \, x^{11} + \frac {2116287}{10} \, x^{10} + 228996 \, x^{9} + \frac {719739}{8} \, x^{8} - 65934 \, x^{7} - 98182 \, x^{6} - \frac {203752}{5} \, x^{5} + 5764 \, x^{4} + \frac {38816}{3} \, x^{3} + 5664 \, x^{2} + 1152 \, 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)^2,x, algorithm="giac")

[Out]

18225*x^12 + 1064340/11*x^11 + 2116287/10*x^10 + 228996*x^9 + 719739/8*x^8 - 65934*x^7 - 98182*x^6 - 203752/5*
x^5 + 5764*x^4 + 38816/3*x^3 + 5664*x^2 + 1152*x

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maple [A]  time = 0.00, size = 60, normalized size = 1.07 \begin {gather*} 18225 x^{12}+\frac {1064340}{11} x^{11}+\frac {2116287}{10} x^{10}+228996 x^{9}+\frac {719739}{8} x^{8}-65934 x^{7}-98182 x^{6}-\frac {203752}{5} x^{5}+5764 x^{4}+\frac {38816}{3} x^{3}+5664 x^{2}+1152 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

18225*x^12+1064340/11*x^11+2116287/10*x^10+228996*x^9+719739/8*x^8-65934*x^7-98182*x^6-203752/5*x^5+5764*x^4+3
8816/3*x^3+5664*x^2+1152*x

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maxima [A]  time = 0.59, size = 59, normalized size = 1.05 \begin {gather*} 18225 \, x^{12} + \frac {1064340}{11} \, x^{11} + \frac {2116287}{10} \, x^{10} + 228996 \, x^{9} + \frac {719739}{8} \, x^{8} - 65934 \, x^{7} - 98182 \, x^{6} - \frac {203752}{5} \, x^{5} + 5764 \, x^{4} + \frac {38816}{3} \, x^{3} + 5664 \, x^{2} + 1152 \, 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)^2,x, algorithm="maxima")

[Out]

18225*x^12 + 1064340/11*x^11 + 2116287/10*x^10 + 228996*x^9 + 719739/8*x^8 - 65934*x^7 - 98182*x^6 - 203752/5*
x^5 + 5764*x^4 + 38816/3*x^3 + 5664*x^2 + 1152*x

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mupad [B]  time = 0.06, size = 59, normalized size = 1.05 \begin {gather*} 18225\,x^{12}+\frac {1064340\,x^{11}}{11}+\frac {2116287\,x^{10}}{10}+228996\,x^9+\frac {719739\,x^8}{8}-65934\,x^7-98182\,x^6-\frac {203752\,x^5}{5}+5764\,x^4+\frac {38816\,x^3}{3}+5664\,x^2+1152\,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)^2,x)

[Out]

1152*x + 5664*x^2 + (38816*x^3)/3 + 5764*x^4 - (203752*x^5)/5 - 98182*x^6 - 65934*x^7 + (719739*x^8)/8 + 22899
6*x^9 + (2116287*x^10)/10 + (1064340*x^11)/11 + 18225*x^12

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sympy [A]  time = 0.08, size = 66, normalized size = 1.18 \begin {gather*} 18225 x^{12} + \frac {1064340 x^{11}}{11} + \frac {2116287 x^{10}}{10} + 228996 x^{9} + \frac {719739 x^{8}}{8} - 65934 x^{7} - 98182 x^{6} - \frac {203752 x^{5}}{5} + 5764 x^{4} + \frac {38816 x^{3}}{3} + 5664 x^{2} + 1152 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)**2,x)

[Out]

18225*x**12 + 1064340*x**11/11 + 2116287*x**10/10 + 228996*x**9 + 719739*x**8/8 - 65934*x**7 - 98182*x**6 - 20
3752*x**5/5 + 5764*x**4 + 38816*x**3/3 + 5664*x**2 + 1152*x

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