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

Optimal. Leaf size=34 \[ -\frac {25}{48} (1-2 x)^6+\frac {11}{4} (1-2 x)^5-\frac {121}{32} (1-2 x)^4 \]

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Rubi [A]  time = 0.01, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {43} \begin {gather*} -\frac {25}{48} (1-2 x)^6+\frac {11}{4} (1-2 x)^5-\frac {121}{32} (1-2 x)^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^3*(3 + 5*x)^2,x]

[Out]

(-121*(1 - 2*x)^4)/32 + (11*(1 - 2*x)^5)/4 - (25*(1 - 2*x)^6)/48

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 (3+5 x)^2 \, dx &=\int \left (\frac {121}{4} (1-2 x)^3-\frac {55}{2} (1-2 x)^4+\frac {25}{4} (1-2 x)^5\right ) \, dx\\ &=-\frac {121}{32} (1-2 x)^4+\frac {11}{4} (1-2 x)^5-\frac {25}{48} (1-2 x)^6\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 35, normalized size = 1.03 \begin {gather*} -\frac {100 x^6}{3}+12 x^5+\frac {69 x^4}{2}-\frac {47 x^3}{3}-12 x^2+9 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^3*(3 + 5*x)^2,x]

[Out]

9*x - 12*x^2 - (47*x^3)/3 + (69*x^4)/2 + 12*x^5 - (100*x^6)/3

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

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.08, size = 29, normalized size = 0.85 \begin {gather*} -\frac {100}{3} x^{6} + 12 x^{5} + \frac {69}{2} x^{4} - \frac {47}{3} x^{3} - 12 x^{2} + 9 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-100/3*x^6 + 12*x^5 + 69/2*x^4 - 47/3*x^3 - 12*x^2 + 9*x

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giac [A]  time = 0.92, size = 29, normalized size = 0.85 \begin {gather*} -\frac {100}{3} \, x^{6} + 12 \, x^{5} + \frac {69}{2} \, x^{4} - \frac {47}{3} \, x^{3} - 12 \, x^{2} + 9 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-100/3*x^6 + 12*x^5 + 69/2*x^4 - 47/3*x^3 - 12*x^2 + 9*x

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maple [A]  time = 0.00, size = 30, normalized size = 0.88 \begin {gather*} -\frac {100}{3} x^{6}+12 x^{5}+\frac {69}{2} x^{4}-\frac {47}{3} x^{3}-12 x^{2}+9 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-100/3*x^6+12*x^5+69/2*x^4-47/3*x^3-12*x^2+9*x

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maxima [A]  time = 0.60, size = 29, normalized size = 0.85 \begin {gather*} -\frac {100}{3} \, x^{6} + 12 \, x^{5} + \frac {69}{2} \, x^{4} - \frac {47}{3} \, x^{3} - 12 \, x^{2} + 9 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-100/3*x^6 + 12*x^5 + 69/2*x^4 - 47/3*x^3 - 12*x^2 + 9*x

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mupad [B]  time = 0.02, size = 29, normalized size = 0.85 \begin {gather*} -\frac {100\,x^6}{3}+12\,x^5+\frac {69\,x^4}{2}-\frac {47\,x^3}{3}-12\,x^2+9\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*x - 1)^3*(5*x + 3)^2,x)

[Out]

9*x - 12*x^2 - (47*x^3)/3 + (69*x^4)/2 + 12*x^5 - (100*x^6)/3

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sympy [A]  time = 0.07, size = 32, normalized size = 0.94 \begin {gather*} - \frac {100 x^{6}}{3} + 12 x^{5} + \frac {69 x^{4}}{2} - \frac {47 x^{3}}{3} - 12 x^{2} + 9 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-100*x**6/3 + 12*x**5 + 69*x**4/2 - 47*x**3/3 - 12*x**2 + 9*x

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