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

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

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Rubi [A]  time = 0.01, antiderivative size = 30, 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 = {77} \begin {gather*} -30 x^5-\frac {205 x^4}{4}-\frac {34 x^3}{3}+\frac {51 x^2}{2}+18 x \end {gather*}

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*}

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Mathematica [A]  time = 0.00, size = 30, normalized size = 1.00 \begin {gather*} -30 x^5-\frac {205 x^4}{4}-\frac {34 x^3}{3}+\frac {51 x^2}{2}+18 x \end {gather*}

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

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.04, size = 24, normalized size = 0.80 \begin {gather*} -30 x^{5} - \frac {205}{4} x^{4} - \frac {34}{3} x^{3} + \frac {51}{2} x^{2} + 18 x \end {gather*}

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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giac [A]  time = 1.21, size = 24, normalized size = 0.80 \begin {gather*} -30 \, x^{5} - \frac {205}{4} \, x^{4} - \frac {34}{3} \, x^{3} + \frac {51}{2} \, x^{2} + 18 \, x \end {gather*}

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

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maple [A]  time = 0.00, size = 25, normalized size = 0.83 \begin {gather*} -30 x^{5}-\frac {205}{4} x^{4}-\frac {34}{3} x^{3}+\frac {51}{2} x^{2}+18 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)*(3*x+2)*(5*x+3)^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 = 0.56, size = 24, normalized size = 0.80 \begin {gather*} -30 \, x^{5} - \frac {205}{4} \, x^{4} - \frac {34}{3} \, x^{3} + \frac {51}{2} \, x^{2} + 18 \, x \end {gather*}

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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mupad [B]  time = 0.02, size = 24, normalized size = 0.80 \begin {gather*} -30\,x^5-\frac {205\,x^4}{4}-\frac {34\,x^3}{3}+\frac {51\,x^2}{2}+18\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.06, size = 27, normalized size = 0.90 \begin {gather*} - 30 x^{5} - \frac {205 x^{4}}{4} - \frac {34 x^{3}}{3} + \frac {51 x^{2}}{2} + 18 x \end {gather*}

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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