3.1346 \(\int (1-2 x)^3 (3+5 x) \, dx\)

Optimal. Leaf size=23 \[ \frac{1}{4} (1-2 x)^5-\frac{11}{16} (1-2 x)^4 \]

[Out]

(-11*(1 - 2*x)^4)/16 + (1 - 2*x)^5/4

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Rubi [A]  time = 0.0051903, 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} \[ \frac{1}{4} (1-2 x)^5-\frac{11}{16} (1-2 x)^4 \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^3*(3 + 5*x),x]

[Out]

(-11*(1 - 2*x)^4)/16 + (1 - 2*x)^5/4

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)^3 (3+5 x) \, dx &=\int \left (\frac{11}{2} (1-2 x)^3-\frac{5}{2} (1-2 x)^4\right ) \, dx\\ &=-\frac{11}{16} (1-2 x)^4+\frac{1}{4} (1-2 x)^5\\ \end{align*}

Mathematica [A]  time = 0.0006997, size = 26, normalized size = 1.13 \[ -8 x^5+9 x^4+2 x^3-\frac{13 x^2}{2}+3 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^3*(3 + 5*x),x]

[Out]

3*x - (13*x^2)/2 + 2*x^3 + 9*x^4 - 8*x^5

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Maple [A]  time = 0.001, size = 25, normalized size = 1.1 \begin{align*} -8\,{x}^{5}+9\,{x}^{4}+2\,{x}^{3}-{\frac{13\,{x}^{2}}{2}}+3\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-8*x^5+9*x^4+2*x^3-13/2*x^2+3*x

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Maxima [A]  time = 1.03892, size = 32, normalized size = 1.39 \begin{align*} -8 \, x^{5} + 9 \, x^{4} + 2 \, x^{3} - \frac{13}{2} \, x^{2} + 3 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-8*x^5 + 9*x^4 + 2*x^3 - 13/2*x^2 + 3*x

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Fricas [A]  time = 1.1303, size = 55, normalized size = 2.39 \begin{align*} -8 x^{5} + 9 x^{4} + 2 x^{3} - \frac{13}{2} x^{2} + 3 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-8*x^5 + 9*x^4 + 2*x^3 - 13/2*x^2 + 3*x

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Sympy [A]  time = 0.059095, size = 24, normalized size = 1.04 \begin{align*} - 8 x^{5} + 9 x^{4} + 2 x^{3} - \frac{13 x^{2}}{2} + 3 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-8*x**5 + 9*x**4 + 2*x**3 - 13*x**2/2 + 3*x

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Giac [A]  time = 2.45975, size = 32, normalized size = 1.39 \begin{align*} -8 \, x^{5} + 9 \, x^{4} + 2 \, x^{3} - \frac{13}{2} \, x^{2} + 3 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-8*x^5 + 9*x^4 + 2*x^3 - 13/2*x^2 + 3*x