3.13.20 \(\int (1-2 x)^3 (2+3 x)^4 (3+5 x)^2 \, dx\)

Optimal. Leaf size=67 \[ -\frac {20}{729} (3 x+2)^{10}+\frac {2180 (3 x+2)^9}{6561}-\frac {4099 (3 x+2)^8}{2916}+\frac {1657}{729} (3 x+2)^7-\frac {1862 (3 x+2)^6}{2187}+\frac {343 (3 x+2)^5}{3645} \]

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Rubi [A]  time = 0.03, 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 = {88} \begin {gather*} -\frac {20}{729} (3 x+2)^{10}+\frac {2180 (3 x+2)^9}{6561}-\frac {4099 (3 x+2)^8}{2916}+\frac {1657}{729} (3 x+2)^7-\frac {1862 (3 x+2)^6}{2187}+\frac {343 (3 x+2)^5}{3645} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^2,x]

[Out]

(343*(2 + 3*x)^5)/3645 - (1862*(2 + 3*x)^6)/2187 + (1657*(2 + 3*x)^7)/729 - (4099*(2 + 3*x)^8)/2916 + (2180*(2
+ 3*x)^9)/6561 - (20*(2 + 3*x)^10)/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)^3 (2+3 x)^4 (3+5 x)^2 \, dx &=\int \left (\frac {343}{243} (2+3 x)^4-\frac {3724}{243} (2+3 x)^5+\frac {11599}{243} (2+3 x)^6-\frac {8198}{243} (2+3 x)^7+\frac {2180}{243} (2+3 x)^8-\frac {200}{243} (2+3 x)^9\right ) \, dx\\ &=\frac {343 (2+3 x)^5}{3645}-\frac {1862 (2+3 x)^6}{2187}+\frac {1657}{729} (2+3 x)^7-\frac {4099 (2+3 x)^8}{2916}+\frac {2180 (2+3 x)^9}{6561}-\frac {20}{729} (2+3 x)^{10}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 57, normalized size = 0.85 \begin {gather*} -1620 x^{10}-4260 x^9-\frac {9531 x^8}{4}+2823 x^7+\frac {10136 x^6}{3}-\frac {399 x^5}{5}-1386 x^4-\frac {1112 x^3}{3}+240 x^2+144 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^2,x]

[Out]

144*x + 240*x^2 - (1112*x^3)/3 - 1386*x^4 - (399*x^5)/5 + (10136*x^6)/3 + 2823*x^7 - (9531*x^8)/4 - 4260*x^9 -
1620*x^10

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x)^3 (2+3 x)^4 (3+5 x)^2 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^2,x]

[Out]

IntegrateAlgebraic[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^2, x]

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fricas [A]  time = 1.03, size = 49, normalized size = 0.73 \begin {gather*} -1620 x^{10} - 4260 x^{9} - \frac {9531}{4} x^{8} + 2823 x^{7} + \frac {10136}{3} x^{6} - \frac {399}{5} x^{5} - 1386 x^{4} - \frac {1112}{3} x^{3} + 240 x^{2} + 144 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^4*(3+5*x)^2,x, algorithm="fricas")

[Out]

-1620*x^10 - 4260*x^9 - 9531/4*x^8 + 2823*x^7 + 10136/3*x^6 - 399/5*x^5 - 1386*x^4 - 1112/3*x^3 + 240*x^2 + 14
4*x

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giac [A]  time = 0.92, size = 49, normalized size = 0.73 \begin {gather*} -1620 \, x^{10} - 4260 \, x^{9} - \frac {9531}{4} \, x^{8} + 2823 \, x^{7} + \frac {10136}{3} \, x^{6} - \frac {399}{5} \, x^{5} - 1386 \, x^{4} - \frac {1112}{3} \, x^{3} + 240 \, x^{2} + 144 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^4*(3+5*x)^2,x, algorithm="giac")

[Out]

-1620*x^10 - 4260*x^9 - 9531/4*x^8 + 2823*x^7 + 10136/3*x^6 - 399/5*x^5 - 1386*x^4 - 1112/3*x^3 + 240*x^2 + 14
4*x

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maple [A]  time = 0.00, size = 50, normalized size = 0.75 \begin {gather*} -1620 x^{10}-4260 x^{9}-\frac {9531}{4} x^{8}+2823 x^{7}+\frac {10136}{3} x^{6}-\frac {399}{5} x^{5}-1386 x^{4}-\frac {1112}{3} x^{3}+240 x^{2}+144 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^3*(3*x+2)^4*(5*x+3)^2,x)

[Out]

-1620*x^10-4260*x^9-9531/4*x^8+2823*x^7+10136/3*x^6-399/5*x^5-1386*x^4-1112/3*x^3+240*x^2+144*x

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maxima [A]  time = 0.48, size = 49, normalized size = 0.73 \begin {gather*} -1620 \, x^{10} - 4260 \, x^{9} - \frac {9531}{4} \, x^{8} + 2823 \, x^{7} + \frac {10136}{3} \, x^{6} - \frac {399}{5} \, x^{5} - 1386 \, x^{4} - \frac {1112}{3} \, x^{3} + 240 \, x^{2} + 144 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^4*(3+5*x)^2,x, algorithm="maxima")

[Out]

-1620*x^10 - 4260*x^9 - 9531/4*x^8 + 2823*x^7 + 10136/3*x^6 - 399/5*x^5 - 1386*x^4 - 1112/3*x^3 + 240*x^2 + 14
4*x

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mupad [B]  time = 0.04, size = 49, normalized size = 0.73 \begin {gather*} -1620\,x^{10}-4260\,x^9-\frac {9531\,x^8}{4}+2823\,x^7+\frac {10136\,x^6}{3}-\frac {399\,x^5}{5}-1386\,x^4-\frac {1112\,x^3}{3}+240\,x^2+144\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*x - 1)^3*(3*x + 2)^4*(5*x + 3)^2,x)

[Out]

144*x + 240*x^2 - (1112*x^3)/3 - 1386*x^4 - (399*x^5)/5 + (10136*x^6)/3 + 2823*x^7 - (9531*x^8)/4 - 4260*x^9 -
1620*x^10

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sympy [A]  time = 0.07, size = 54, normalized size = 0.81 \begin {gather*} - 1620 x^{10} - 4260 x^{9} - \frac {9531 x^{8}}{4} + 2823 x^{7} + \frac {10136 x^{6}}{3} - \frac {399 x^{5}}{5} - 1386 x^{4} - \frac {1112 x^{3}}{3} + 240 x^{2} + 144 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**3*(2+3*x)**4*(3+5*x)**2,x)

[Out]

-1620*x**10 - 4260*x**9 - 9531*x**8/4 + 2823*x**7 + 10136*x**6/3 - 399*x**5/5 - 1386*x**4 - 1112*x**3/3 + 240*
x**2 + 144*x

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