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

Optimal. Leaf size=49 \[ \frac {1125 x^8}{2}+\frac {9600 x^7}{7}+\frac {4685 x^6}{6}-\frac {3083 x^5}{5}-\frac {3181 x^4}{4}-87 x^3+216 x^2+108 x \]

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Rubi [A]  time = 0.02, antiderivative size = 49, 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 {1125 x^8}{2}+\frac {9600 x^7}{7}+\frac {4685 x^6}{6}-\frac {3083 x^5}{5}-\frac {3181 x^4}{4}-87 x^3+216 x^2+108 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

108*x + 216*x^2 - 87*x^3 - (3181*x^4)/4 - (3083*x^5)/5 + (4685*x^6)/6 + (9600*x^7)/7 + (1125*x^8)/2

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)^2 (3+5 x)^3 \, dx &=\int \left (108+432 x-261 x^2-3181 x^3-3083 x^4+4685 x^5+9600 x^6+4500 x^7\right ) \, dx\\ &=108 x+216 x^2-87 x^3-\frac {3181 x^4}{4}-\frac {3083 x^5}{5}+\frac {4685 x^6}{6}+\frac {9600 x^7}{7}+\frac {1125 x^8}{2}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 49, normalized size = 1.00 \begin {gather*} \frac {1125 x^8}{2}+\frac {9600 x^7}{7}+\frac {4685 x^6}{6}-\frac {3083 x^5}{5}-\frac {3181 x^4}{4}-87 x^3+216 x^2+108 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

108*x + 216*x^2 - 87*x^3 - (3181*x^4)/4 - (3083*x^5)/5 + (4685*x^6)/6 + (9600*x^7)/7 + (1125*x^8)/2

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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)^2 (3+5 x)^3 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.24, size = 39, normalized size = 0.80 \begin {gather*} \frac {1125}{2} x^{8} + \frac {9600}{7} x^{7} + \frac {4685}{6} x^{6} - \frac {3083}{5} x^{5} - \frac {3181}{4} x^{4} - 87 x^{3} + 216 x^{2} + 108 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1125/2*x^8 + 9600/7*x^7 + 4685/6*x^6 - 3083/5*x^5 - 3181/4*x^4 - 87*x^3 + 216*x^2 + 108*x

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giac [A]  time = 0.80, size = 39, normalized size = 0.80 \begin {gather*} \frac {1125}{2} \, x^{8} + \frac {9600}{7} \, x^{7} + \frac {4685}{6} \, x^{6} - \frac {3083}{5} \, x^{5} - \frac {3181}{4} \, x^{4} - 87 \, x^{3} + 216 \, x^{2} + 108 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1125/2*x^8 + 9600/7*x^7 + 4685/6*x^6 - 3083/5*x^5 - 3181/4*x^4 - 87*x^3 + 216*x^2 + 108*x

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maple [A]  time = 0.00, size = 40, normalized size = 0.82 \begin {gather*} \frac {1125}{2} x^{8}+\frac {9600}{7} x^{7}+\frac {4685}{6} x^{6}-\frac {3083}{5} x^{5}-\frac {3181}{4} x^{4}-87 x^{3}+216 x^{2}+108 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

108*x+216*x^2-87*x^3-3181/4*x^4-3083/5*x^5+4685/6*x^6+9600/7*x^7+1125/2*x^8

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maxima [A]  time = 0.61, size = 39, normalized size = 0.80 \begin {gather*} \frac {1125}{2} \, x^{8} + \frac {9600}{7} \, x^{7} + \frac {4685}{6} \, x^{6} - \frac {3083}{5} \, x^{5} - \frac {3181}{4} \, x^{4} - 87 \, x^{3} + 216 \, x^{2} + 108 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1125/2*x^8 + 9600/7*x^7 + 4685/6*x^6 - 3083/5*x^5 - 3181/4*x^4 - 87*x^3 + 216*x^2 + 108*x

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mupad [B]  time = 0.03, size = 39, normalized size = 0.80 \begin {gather*} \frac {1125\,x^8}{2}+\frac {9600\,x^7}{7}+\frac {4685\,x^6}{6}-\frac {3083\,x^5}{5}-\frac {3181\,x^4}{4}-87\,x^3+216\,x^2+108\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

108*x + 216*x^2 - 87*x^3 - (3181*x^4)/4 - (3083*x^5)/5 + (4685*x^6)/6 + (9600*x^7)/7 + (1125*x^8)/2

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sympy [A]  time = 0.07, size = 46, normalized size = 0.94 \begin {gather*} \frac {1125 x^{8}}{2} + \frac {9600 x^{7}}{7} + \frac {4685 x^{6}}{6} - \frac {3083 x^{5}}{5} - \frac {3181 x^{4}}{4} - 87 x^{3} + 216 x^{2} + 108 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1125*x**8/2 + 9600*x**7/7 + 4685*x**6/6 - 3083*x**5/5 - 3181*x**4/4 - 87*x**3 + 216*x**2 + 108*x

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