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

Optimal. Leaf size=31 \[ -75 x^6-183 x^5-128 x^4+\frac {85 x^3}{3}+78 x^2+36 x \]

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Rubi [A]  time = 0.01, antiderivative size = 31, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} -75 x^6-183 x^5-128 x^4+\frac {85 x^3}{3}+78 x^2+36 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

36*x + 78*x^2 + (85*x^3)/3 - 128*x^4 - 183*x^5 - 75*x^6

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)^2 (3+5 x)^2 \, dx &=\int \left (36+156 x+85 x^2-512 x^3-915 x^4-450 x^5\right ) \, dx\\ &=36 x+78 x^2+\frac {85 x^3}{3}-128 x^4-183 x^5-75 x^6\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 31, normalized size = 1.00 \begin {gather*} -75 x^6-183 x^5-128 x^4+\frac {85 x^3}{3}+78 x^2+36 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

36*x + 78*x^2 + (85*x^3)/3 - 128*x^4 - 183*x^5 - 75*x^6

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x) (2+3 x)^2 (3+5 x)^2 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.05, size = 29, normalized size = 0.94 \begin {gather*} -75 x^{6} - 183 x^{5} - 128 x^{4} + \frac {85}{3} x^{3} + 78 x^{2} + 36 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-75*x^6 - 183*x^5 - 128*x^4 + 85/3*x^3 + 78*x^2 + 36*x

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giac [A]  time = 1.21, size = 29, normalized size = 0.94 \begin {gather*} -75 \, x^{6} - 183 \, x^{5} - 128 \, x^{4} + \frac {85}{3} \, x^{3} + 78 \, x^{2} + 36 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-75*x^6 - 183*x^5 - 128*x^4 + 85/3*x^3 + 78*x^2 + 36*x

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maple [A]  time = 0.00, size = 30, normalized size = 0.97 \begin {gather*} -75 x^{6}-183 x^{5}-128 x^{4}+\frac {85}{3} x^{3}+78 x^{2}+36 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

36*x+78*x^2+85/3*x^3-128*x^4-183*x^5-75*x^6

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maxima [A]  time = 0.47, size = 29, normalized size = 0.94 \begin {gather*} -75 \, x^{6} - 183 \, x^{5} - 128 \, x^{4} + \frac {85}{3} \, x^{3} + 78 \, x^{2} + 36 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-75*x^6 - 183*x^5 - 128*x^4 + 85/3*x^3 + 78*x^2 + 36*x

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mupad [B]  time = 0.02, size = 29, normalized size = 0.94 \begin {gather*} -75\,x^6-183\,x^5-128\,x^4+\frac {85\,x^3}{3}+78\,x^2+36\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

36*x + 78*x^2 + (85*x^3)/3 - 128*x^4 - 183*x^5 - 75*x^6

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sympy [A]  time = 0.07, size = 29, normalized size = 0.94 \begin {gather*} - 75 x^{6} - 183 x^{5} - 128 x^{4} + \frac {85 x^{3}}{3} + 78 x^{2} + 36 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-75*x**6 - 183*x**5 - 128*x**4 + 85*x**3/3 + 78*x**2 + 36*x

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