3.1165 \(\int (1-2 x) (2+3 x) (3+5 x)^2 \, dx\)

Optimal. Leaf size=30 \[ -30 x^5-\frac{205 x^4}{4}-\frac{34 x^3}{3}+\frac{51 x^2}{2}+18 x \]

[Out]

18*x + (51*x^2)/2 - (34*x^3)/3 - (205*x^4)/4 - 30*x^5

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Rubi [A]  time = 0.0117571, antiderivative size = 30, 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} \[ -30 x^5-\frac{205 x^4}{4}-\frac{34 x^3}{3}+\frac{51 x^2}{2}+18 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

18*x + (51*x^2)/2 - (34*x^3)/3 - (205*x^4)/4 - 30*x^5

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) (2+3 x) (3+5 x)^2 \, dx &=\int \left (18+51 x-34 x^2-205 x^3-150 x^4\right ) \, dx\\ &=18 x+\frac{51 x^2}{2}-\frac{34 x^3}{3}-\frac{205 x^4}{4}-30 x^5\\ \end{align*}

Mathematica [A]  time = 0.0006473, size = 30, normalized size = 1. \[ -30 x^5-\frac{205 x^4}{4}-\frac{34 x^3}{3}+\frac{51 x^2}{2}+18 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

18*x + (51*x^2)/2 - (34*x^3)/3 - (205*x^4)/4 - 30*x^5

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Maple [A]  time = 0.001, size = 25, normalized size = 0.8 \begin{align*} 18\,x+{\frac{51\,{x}^{2}}{2}}-{\frac{34\,{x}^{3}}{3}}-{\frac{205\,{x}^{4}}{4}}-30\,{x}^{5} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

18*x+51/2*x^2-34/3*x^3-205/4*x^4-30*x^5

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Maxima [A]  time = 1.34398, size = 32, normalized size = 1.07 \begin{align*} -30 \, x^{5} - \frac{205}{4} \, x^{4} - \frac{34}{3} \, x^{3} + \frac{51}{2} \, x^{2} + 18 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-30*x^5 - 205/4*x^4 - 34/3*x^3 + 51/2*x^2 + 18*x

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Fricas [A]  time = 1.60422, size = 68, normalized size = 2.27 \begin{align*} -30 x^{5} - \frac{205}{4} x^{4} - \frac{34}{3} x^{3} + \frac{51}{2} x^{2} + 18 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-30*x^5 - 205/4*x^4 - 34/3*x^3 + 51/2*x^2 + 18*x

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Sympy [A]  time = 0.055748, size = 27, normalized size = 0.9 \begin{align*} - 30 x^{5} - \frac{205 x^{4}}{4} - \frac{34 x^{3}}{3} + \frac{51 x^{2}}{2} + 18 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-30*x**5 - 205*x**4/4 - 34*x**3/3 + 51*x**2/2 + 18*x

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Giac [A]  time = 2.30499, size = 32, normalized size = 1.07 \begin{align*} -30 \, x^{5} - \frac{205}{4} \, x^{4} - \frac{34}{3} \, x^{3} + \frac{51}{2} \, x^{2} + 18 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-30*x^5 - 205/4*x^4 - 34/3*x^3 + 51/2*x^2 + 18*x