3.1363 \(\int (1-2 x)^3 (3+5 x)^2 \, dx\)

Optimal. Leaf size=34 \[ -\frac{25}{48} (1-2 x)^6+\frac{11}{4} (1-2 x)^5-\frac{121}{32} (1-2 x)^4 \]

[Out]

(-121*(1 - 2*x)^4)/32 + (11*(1 - 2*x)^5)/4 - (25*(1 - 2*x)^6)/48

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Rubi [A]  time = 0.0143311, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {43} \[ -\frac{25}{48} (1-2 x)^6+\frac{11}{4} (1-2 x)^5-\frac{121}{32} (1-2 x)^4 \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^3*(3 + 5*x)^2,x]

[Out]

(-121*(1 - 2*x)^4)/32 + (11*(1 - 2*x)^5)/4 - (25*(1 - 2*x)^6)/48

Rule 43

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rubi steps

\begin{align*} \int (1-2 x)^3 (3+5 x)^2 \, dx &=\int \left (\frac{121}{4} (1-2 x)^3-\frac{55}{2} (1-2 x)^4+\frac{25}{4} (1-2 x)^5\right ) \, dx\\ &=-\frac{121}{32} (1-2 x)^4+\frac{11}{4} (1-2 x)^5-\frac{25}{48} (1-2 x)^6\\ \end{align*}

Mathematica [A]  time = 0.0008315, size = 35, normalized size = 1.03 \[ -\frac{100 x^6}{3}+12 x^5+\frac{69 x^4}{2}-\frac{47 x^3}{3}-12 x^2+9 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^3*(3 + 5*x)^2,x]

[Out]

9*x - 12*x^2 - (47*x^3)/3 + (69*x^4)/2 + 12*x^5 - (100*x^6)/3

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Maple [A]  time = 0.001, size = 30, normalized size = 0.9 \begin{align*} -{\frac{100\,{x}^{6}}{3}}+12\,{x}^{5}+{\frac{69\,{x}^{4}}{2}}-{\frac{47\,{x}^{3}}{3}}-12\,{x}^{2}+9\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-100/3*x^6+12*x^5+69/2*x^4-47/3*x^3-12*x^2+9*x

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Maxima [A]  time = 1.88086, size = 39, normalized size = 1.15 \begin{align*} -\frac{100}{3} \, x^{6} + 12 \, x^{5} + \frac{69}{2} \, x^{4} - \frac{47}{3} \, x^{3} - 12 \, x^{2} + 9 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-100/3*x^6 + 12*x^5 + 69/2*x^4 - 47/3*x^3 - 12*x^2 + 9*x

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Fricas [A]  time = 1.09641, size = 78, normalized size = 2.29 \begin{align*} -\frac{100}{3} x^{6} + 12 x^{5} + \frac{69}{2} x^{4} - \frac{47}{3} x^{3} - 12 x^{2} + 9 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-100/3*x^6 + 12*x^5 + 69/2*x^4 - 47/3*x^3 - 12*x^2 + 9*x

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Sympy [A]  time = 0.061568, size = 32, normalized size = 0.94 \begin{align*} - \frac{100 x^{6}}{3} + 12 x^{5} + \frac{69 x^{4}}{2} - \frac{47 x^{3}}{3} - 12 x^{2} + 9 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-100*x**6/3 + 12*x**5 + 69*x**4/2 - 47*x**3/3 - 12*x**2 + 9*x

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Giac [A]  time = 3.61225, size = 39, normalized size = 1.15 \begin{align*} -\frac{100}{3} \, x^{6} + 12 \, x^{5} + \frac{69}{2} \, x^{4} - \frac{47}{3} \, x^{3} - 12 \, x^{2} + 9 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-100/3*x^6 + 12*x^5 + 69/2*x^4 - 47/3*x^3 - 12*x^2 + 9*x