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

Optimal. Leaf size=46 \[ -\frac {600 x^7}{7}-\frac {110 x^6}{3}+\frac {534 x^5}{5}+\frac {135 x^4}{4}-\frac {166 x^3}{3}-\frac {21 x^2}{2}+18 x \]

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Rubi [A]  time = 0.02, antiderivative size = 46, 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 {600 x^7}{7}-\frac {110 x^6}{3}+\frac {534 x^5}{5}+\frac {135 x^4}{4}-\frac {166 x^3}{3}-\frac {21 x^2}{2}+18 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

18*x - (21*x^2)/2 - (166*x^3)/3 + (135*x^4)/4 + (534*x^5)/5 - (110*x^6)/3 - (600*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) (3+5 x)^2 \, dx &=\int \left (18-21 x-166 x^2+135 x^3+534 x^4-220 x^5-600 x^6\right ) \, dx\\ &=18 x-\frac {21 x^2}{2}-\frac {166 x^3}{3}+\frac {135 x^4}{4}+\frac {534 x^5}{5}-\frac {110 x^6}{3}-\frac {600 x^7}{7}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 46, normalized size = 1.00 \begin {gather*} -\frac {600 x^7}{7}-\frac {110 x^6}{3}+\frac {534 x^5}{5}+\frac {135 x^4}{4}-\frac {166 x^3}{3}-\frac {21 x^2}{2}+18 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

18*x - (21*x^2)/2 - (166*x^3)/3 + (135*x^4)/4 + (534*x^5)/5 - (110*x^6)/3 - (600*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) (3+5 x)^2 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.02, size = 34, normalized size = 0.74 \begin {gather*} -\frac {600}{7} x^{7} - \frac {110}{3} x^{6} + \frac {534}{5} x^{5} + \frac {135}{4} x^{4} - \frac {166}{3} x^{3} - \frac {21}{2} x^{2} + 18 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-600/7*x^7 - 110/3*x^6 + 534/5*x^5 + 135/4*x^4 - 166/3*x^3 - 21/2*x^2 + 18*x

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giac [A]  time = 0.82, size = 34, normalized size = 0.74 \begin {gather*} -\frac {600}{7} \, x^{7} - \frac {110}{3} \, x^{6} + \frac {534}{5} \, x^{5} + \frac {135}{4} \, x^{4} - \frac {166}{3} \, x^{3} - \frac {21}{2} \, x^{2} + 18 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-600/7*x^7 - 110/3*x^6 + 534/5*x^5 + 135/4*x^4 - 166/3*x^3 - 21/2*x^2 + 18*x

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maple [A]  time = 0.00, size = 35, normalized size = 0.76 \begin {gather*} -\frac {600}{7} x^{7}-\frac {110}{3} x^{6}+\frac {534}{5} x^{5}+\frac {135}{4} x^{4}-\frac {166}{3} x^{3}-\frac {21}{2} x^{2}+18 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

18*x-21/2*x^2-166/3*x^3+135/4*x^4+534/5*x^5-110/3*x^6-600/7*x^7

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maxima [A]  time = 0.50, size = 34, normalized size = 0.74 \begin {gather*} -\frac {600}{7} \, x^{7} - \frac {110}{3} \, x^{6} + \frac {534}{5} \, x^{5} + \frac {135}{4} \, x^{4} - \frac {166}{3} \, x^{3} - \frac {21}{2} \, x^{2} + 18 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-600/7*x^7 - 110/3*x^6 + 534/5*x^5 + 135/4*x^4 - 166/3*x^3 - 21/2*x^2 + 18*x

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mupad [B]  time = 0.03, size = 34, normalized size = 0.74 \begin {gather*} -\frac {600\,x^7}{7}-\frac {110\,x^6}{3}+\frac {534\,x^5}{5}+\frac {135\,x^4}{4}-\frac {166\,x^3}{3}-\frac {21\,x^2}{2}+18\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

18*x - (21*x^2)/2 - (166*x^3)/3 + (135*x^4)/4 + (534*x^5)/5 - (110*x^6)/3 - (600*x^7)/7

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sympy [A]  time = 0.07, size = 42, normalized size = 0.91 \begin {gather*} - \frac {600 x^{7}}{7} - \frac {110 x^{6}}{3} + \frac {534 x^{5}}{5} + \frac {135 x^{4}}{4} - \frac {166 x^{3}}{3} - \frac {21 x^{2}}{2} + 18 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-600*x**7/7 - 110*x**6/3 + 534*x**5/5 + 135*x**4/4 - 166*x**3/3 - 21*x**2/2 + 18*x

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