3.13.43 \(\int (1-2 x)^2 (2+3 x) (3+5 x) \, dx\) [1243]

Optimal. Leaf size=28 \[ 6 x-\frac {5 x^2}{2}-\frac {37 x^3}{3}+4 x^4+12 x^5 \]

[Out]

6*x-5/2*x^2-37/3*x^3+4*x^4+12*x^5

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Rubi [A]
time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.00, 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 = {78} \begin {gather*} 12 x^5+4 x^4-\frac {37 x^3}{3}-\frac {5 x^2}{2}+6 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

6*x - (5*x^2)/2 - (37*x^3)/3 + 4*x^4 + 12*x^5

Rule 78

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 (2+3 x) (3+5 x) \, dx &=\int \left (6-5 x-37 x^2+16 x^3+60 x^4\right ) \, dx\\ &=6 x-\frac {5 x^2}{2}-\frac {37 x^3}{3}+4 x^4+12 x^5\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 28, normalized size = 1.00 \begin {gather*} 6 x-\frac {5 x^2}{2}-\frac {37 x^3}{3}+4 x^4+12 x^5 \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

6*x - (5*x^2)/2 - (37*x^3)/3 + 4*x^4 + 12*x^5

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Maple [A]
time = 0.08, size = 25, normalized size = 0.89

method	result	size
gosper	\(\frac {x \left (72 x^{4}+24 x^{3}-74 x^{2}-15 x +36\right )}{6}\)	\(24\)
default	\(6 x -\frac {5}{2} x^{2}-\frac {37}{3} x^{3}+4 x^{4}+12 x^{5}\)	\(25\)
norman	\(6 x -\frac {5}{2} x^{2}-\frac {37}{3} x^{3}+4 x^{4}+12 x^{5}\)	\(25\)
risch	\(6 x -\frac {5}{2} x^{2}-\frac {37}{3} x^{3}+4 x^{4}+12 x^{5}\)	\(25\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

6*x-5/2*x^2-37/3*x^3+4*x^4+12*x^5

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Maxima [A]
time = 0.28, size = 24, normalized size = 0.86 \begin {gather*} 12 \, x^{5} + 4 \, x^{4} - \frac {37}{3} \, x^{3} - \frac {5}{2} \, x^{2} + 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

12*x^5 + 4*x^4 - 37/3*x^3 - 5/2*x^2 + 6*x

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Fricas [A]
time = 1.03, size = 24, normalized size = 0.86 \begin {gather*} 12 \, x^{5} + 4 \, x^{4} - \frac {37}{3} \, x^{3} - \frac {5}{2} \, x^{2} + 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

12*x^5 + 4*x^4 - 37/3*x^3 - 5/2*x^2 + 6*x

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Sympy [A]
time = 0.03, size = 26, normalized size = 0.93 \begin {gather*} 12 x^{5} + 4 x^{4} - \frac {37 x^{3}}{3} - \frac {5 x^{2}}{2} + 6 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

12*x**5 + 4*x**4 - 37*x**3/3 - 5*x**2/2 + 6*x

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Giac [A]
time = 0.83, size = 24, normalized size = 0.86 \begin {gather*} 12 \, x^{5} + 4 \, x^{4} - \frac {37}{3} \, x^{3} - \frac {5}{2} \, x^{2} + 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

12*x^5 + 4*x^4 - 37/3*x^3 - 5/2*x^2 + 6*x

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Mupad [B]
time = 0.02, size = 24, normalized size = 0.86 \begin {gather*} 12\,x^5+4\,x^4-\frac {37\,x^3}{3}-\frac {5\,x^2}{2}+6\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

6*x - (5*x^2)/2 - (37*x^3)/3 + 4*x^4 + 12*x^5

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