3.1345 \(\int (1-2 x)^3 (2+3 x) (3+5 x) \, dx\)

Optimal. Leaf size=34 \[ -\frac{5}{16} (1-2 x)^6+\frac{17}{10} (1-2 x)^5-\frac{77}{32} (1-2 x)^4 \]

[Out]

(-77*(1 - 2*x)^4)/32 + (17*(1 - 2*x)^5)/10 - (5*(1 - 2*x)^6)/16

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Rubi [A]  time = 0.0144095, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {77} \[ -\frac{5}{16} (1-2 x)^6+\frac{17}{10} (1-2 x)^5-\frac{77}{32} (1-2 x)^4 \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-77*(1 - 2*x)^4)/32 + (17*(1 - 2*x)^5)/10 - (5*(1 - 2*x)^6)/16

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) \, dx &=\int \left (\frac{77}{4} (1-2 x)^3-17 (1-2 x)^4+\frac{15}{4} (1-2 x)^5\right ) \, dx\\ &=-\frac{77}{32} (1-2 x)^4+\frac{17}{10} (1-2 x)^5-\frac{5}{16} (1-2 x)^6\\ \end{align*}

Mathematica [A]  time = 0.0007683, size = 35, normalized size = 1.03 \[ -20 x^6+\frac{28 x^5}{5}+\frac{45 x^4}{2}-9 x^3-\frac{17 x^2}{2}+6 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

6*x - (17*x^2)/2 - 9*x^3 + (45*x^4)/2 + (28*x^5)/5 - 20*x^6

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Maple [A]  time = 0., size = 30, normalized size = 0.9 \begin{align*} -20\,{x}^{6}+{\frac{28\,{x}^{5}}{5}}+{\frac{45\,{x}^{4}}{2}}-9\,{x}^{3}-{\frac{17\,{x}^{2}}{2}}+6\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-20*x^6+28/5*x^5+45/2*x^4-9*x^3-17/2*x^2+6*x

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Maxima [A]  time = 1.28086, size = 39, normalized size = 1.15 \begin{align*} -20 \, x^{6} + \frac{28}{5} \, x^{5} + \frac{45}{2} \, x^{4} - 9 \, x^{3} - \frac{17}{2} \, x^{2} + 6 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-20*x^6 + 28/5*x^5 + 45/2*x^4 - 9*x^3 - 17/2*x^2 + 6*x

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Fricas [A]  time = 1.13918, size = 76, normalized size = 2.24 \begin{align*} -20 x^{6} + \frac{28}{5} x^{5} + \frac{45}{2} x^{4} - 9 x^{3} - \frac{17}{2} x^{2} + 6 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-20*x^6 + 28/5*x^5 + 45/2*x^4 - 9*x^3 - 17/2*x^2 + 6*x

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Sympy [A]  time = 0.05735, size = 32, normalized size = 0.94 \begin{align*} - 20 x^{6} + \frac{28 x^{5}}{5} + \frac{45 x^{4}}{2} - 9 x^{3} - \frac{17 x^{2}}{2} + 6 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-20*x**6 + 28*x**5/5 + 45*x**4/2 - 9*x**3 - 17*x**2/2 + 6*x

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Giac [A]  time = 2.32989, size = 39, normalized size = 1.15 \begin{align*} -20 \, x^{6} + \frac{28}{5} \, x^{5} + \frac{45}{2} \, x^{4} - 9 \, x^{3} - \frac{17}{2} \, x^{2} + 6 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-20*x^6 + 28/5*x^5 + 45/2*x^4 - 9*x^3 - 17/2*x^2 + 6*x