3.1151 \(\int (1-2 x) (3+5 x) \, dx\)

Optimal. Leaf size=18 \[ -\frac{10 x^3}{3}-\frac{x^2}{2}+3 x \]

[Out]

3*x - x^2/2 - (10*x^3)/3

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Rubi [A]  time = 0.006176, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {43} \[ -\frac{10 x^3}{3}-\frac{x^2}{2}+3 x \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)*(3 + 5*x),x]

[Out]

3*x - x^2/2 - (10*x^3)/3

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+5 x) \, dx &=\int \left (3-x-10 x^2\right ) \, dx\\ &=3 x-\frac{x^2}{2}-\frac{10 x^3}{3}\\ \end{align*}

Mathematica [A]  time = 0.000789, size = 18, normalized size = 1. \[ -\frac{10 x^3}{3}-\frac{x^2}{2}+3 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)*(3 + 5*x),x]

[Out]

3*x - x^2/2 - (10*x^3)/3

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Maple [A]  time = 0., size = 15, normalized size = 0.8 \begin{align*} 3\,x-{\frac{{x}^{2}}{2}}-{\frac{10\,{x}^{3}}{3}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3*x-1/2*x^2-10/3*x^3

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Maxima [A]  time = 2.66102, size = 19, normalized size = 1.06 \begin{align*} -\frac{10}{3} \, x^{3} - \frac{1}{2} \, x^{2} + 3 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-10/3*x^3 - 1/2*x^2 + 3*x

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Fricas [A]  time = 1.27703, size = 36, normalized size = 2. \begin{align*} -\frac{10}{3} x^{3} - \frac{1}{2} x^{2} + 3 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-10/3*x^3 - 1/2*x^2 + 3*x

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Sympy [A]  time = 0.050122, size = 14, normalized size = 0.78 \begin{align*} - \frac{10 x^{3}}{3} - \frac{x^{2}}{2} + 3 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-10*x**3/3 - x**2/2 + 3*x

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Giac [A]  time = 3.29494, size = 19, normalized size = 1.06 \begin{align*} -\frac{10}{3} \, x^{3} - \frac{1}{2} \, x^{2} + 3 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-10/3*x^3 - 1/2*x^2 + 3*x