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

Optimal. Leaf size=40 \[ -\frac {360 x^7}{7}-26 x^6+\frac {326 x^5}{5}+\frac {99 x^4}{4}-35 x^3-8 x^2+12 x \]

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Rubi [A]  time = 0.02, antiderivative size = 40, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} -\frac {360 x^7}{7}-26 x^6+\frac {326 x^5}{5}+\frac {99 x^4}{4}-35 x^3-8 x^2+12 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

12*x - 8*x^2 - 35*x^3 + (99*x^4)/4 + (326*x^5)/5 - 26*x^6 - (360*x^7)/7

Rule 77

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps

\begin {align*} \int (1-2 x)^3 (2+3 x)^2 (3+5 x) \, dx &=\int \left (12-16 x-105 x^2+99 x^3+326 x^4-156 x^5-360 x^6\right ) \, dx\\ &=12 x-8 x^2-35 x^3+\frac {99 x^4}{4}+\frac {326 x^5}{5}-26 x^6-\frac {360 x^7}{7}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 40, normalized size = 1.00 \begin {gather*} -\frac {360 x^7}{7}-26 x^6+\frac {326 x^5}{5}+\frac {99 x^4}{4}-35 x^3-8 x^2+12 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

12*x - 8*x^2 - 35*x^3 + (99*x^4)/4 + (326*x^5)/5 - 26*x^6 - (360*x^7)/7

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

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.92, size = 34, normalized size = 0.85 \begin {gather*} -\frac {360}{7} x^{7} - 26 x^{6} + \frac {326}{5} x^{5} + \frac {99}{4} x^{4} - 35 x^{3} - 8 x^{2} + 12 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-360/7*x^7 - 26*x^6 + 326/5*x^5 + 99/4*x^4 - 35*x^3 - 8*x^2 + 12*x

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giac [A]  time = 0.96, size = 34, normalized size = 0.85 \begin {gather*} -\frac {360}{7} \, x^{7} - 26 \, x^{6} + \frac {326}{5} \, x^{5} + \frac {99}{4} \, x^{4} - 35 \, x^{3} - 8 \, x^{2} + 12 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-360/7*x^7 - 26*x^6 + 326/5*x^5 + 99/4*x^4 - 35*x^3 - 8*x^2 + 12*x

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maple [A]  time = 0.00, size = 35, normalized size = 0.88 \begin {gather*} -\frac {360}{7} x^{7}-26 x^{6}+\frac {326}{5} x^{5}+\frac {99}{4} x^{4}-35 x^{3}-8 x^{2}+12 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

12*x-8*x^2-35*x^3+99/4*x^4+326/5*x^5-26*x^6-360/7*x^7

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maxima [A]  time = 0.62, size = 34, normalized size = 0.85 \begin {gather*} -\frac {360}{7} \, x^{7} - 26 \, x^{6} + \frac {326}{5} \, x^{5} + \frac {99}{4} \, x^{4} - 35 \, x^{3} - 8 \, x^{2} + 12 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-360/7*x^7 - 26*x^6 + 326/5*x^5 + 99/4*x^4 - 35*x^3 - 8*x^2 + 12*x

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mupad [B]  time = 0.03, size = 34, normalized size = 0.85 \begin {gather*} -\frac {360\,x^7}{7}-26\,x^6+\frac {326\,x^5}{5}+\frac {99\,x^4}{4}-35\,x^3-8\,x^2+12\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

12*x - 8*x^2 - 35*x^3 + (99*x^4)/4 + (326*x^5)/5 - 26*x^6 - (360*x^7)/7

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sympy [A]  time = 0.07, size = 37, normalized size = 0.92 \begin {gather*} - \frac {360 x^{7}}{7} - 26 x^{6} + \frac {326 x^{5}}{5} + \frac {99 x^{4}}{4} - 35 x^{3} - 8 x^{2} + 12 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-360*x**7/7 - 26*x**6 + 326*x**5/5 + 99*x**4/4 - 35*x**3 - 8*x**2 + 12*x

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