3.1244 \(\int (1-2 x)^2 (3+5 x) \, dx\)

Optimal. Leaf size=23 \[ 5 x^4-\frac{8 x^3}{3}-\frac{7 x^2}{2}+3 x \]

[Out]

3*x - (7*x^2)/2 - (8*x^3)/3 + 5*x^4

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Rubi [A]  time = 0.0080378, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {43} \[ 5 x^4-\frac{8 x^3}{3}-\frac{7 x^2}{2}+3 x \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^2*(3 + 5*x),x]

[Out]

3*x - (7*x^2)/2 - (8*x^3)/3 + 5*x^4

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)^2 (3+5 x) \, dx &=\int \left (3-7 x-8 x^2+20 x^3\right ) \, dx\\ &=3 x-\frac{7 x^2}{2}-\frac{8 x^3}{3}+5 x^4\\ \end{align*}

Mathematica [A]  time = 0.0006351, size = 23, normalized size = 1. \[ 5 x^4-\frac{8 x^3}{3}-\frac{7 x^2}{2}+3 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^2*(3 + 5*x),x]

[Out]

3*x - (7*x^2)/2 - (8*x^3)/3 + 5*x^4

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Maple [A]  time = 0.001, size = 20, normalized size = 0.9 \begin{align*} 3\,x-{\frac{7\,{x}^{2}}{2}}-{\frac{8\,{x}^{3}}{3}}+5\,{x}^{4} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3*x-7/2*x^2-8/3*x^3+5*x^4

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Maxima [A]  time = 2.51226, size = 26, normalized size = 1.13 \begin{align*} 5 \, x^{4} - \frac{8}{3} \, x^{3} - \frac{7}{2} \, x^{2} + 3 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

5*x^4 - 8/3*x^3 - 7/2*x^2 + 3*x

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Fricas [A]  time = 1.33897, size = 45, normalized size = 1.96 \begin{align*} 5 x^{4} - \frac{8}{3} x^{3} - \frac{7}{2} x^{2} + 3 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

5*x^4 - 8/3*x^3 - 7/2*x^2 + 3*x

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Sympy [A]  time = 0.057019, size = 20, normalized size = 0.87 \begin{align*} 5 x^{4} - \frac{8 x^{3}}{3} - \frac{7 x^{2}}{2} + 3 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

5*x**4 - 8*x**3/3 - 7*x**2/2 + 3*x

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Giac [A]  time = 3.03925, size = 26, normalized size = 1.13 \begin{align*} 5 \, x^{4} - \frac{8}{3} \, x^{3} - \frac{7}{2} \, x^{2} + 3 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

5*x^4 - 8/3*x^3 - 7/2*x^2 + 3*x