3.1241 \(\int (1-2 x)^2 (2+3 x)^3 (3+5 x) \, dx\)

Optimal. Leaf size=42 \[ \frac{540 x^7}{7}+144 x^6+\frac{99 x^5}{5}-\frac{425 x^4}{4}-\frac{154 x^3}{3}+26 x^2+24 x \]

[Out]

24*x + 26*x^2 - (154*x^3)/3 - (425*x^4)/4 + (99*x^5)/5 + 144*x^6 + (540*x^7)/7

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Rubi [A]  time = 0.0156931, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ \frac{540 x^7}{7}+144 x^6+\frac{99 x^5}{5}-\frac{425 x^4}{4}-\frac{154 x^3}{3}+26 x^2+24 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

24*x + 26*x^2 - (154*x^3)/3 - (425*x^4)/4 + (99*x^5)/5 + 144*x^6 + (540*x^7)/7

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 (2+3 x)^3 (3+5 x) \, dx &=\int \left (24+52 x-154 x^2-425 x^3+99 x^4+864 x^5+540 x^6\right ) \, dx\\ &=24 x+26 x^2-\frac{154 x^3}{3}-\frac{425 x^4}{4}+\frac{99 x^5}{5}+144 x^6+\frac{540 x^7}{7}\\ \end{align*}

Mathematica [A]  time = 0.000846, size = 42, normalized size = 1. \[ \frac{540 x^7}{7}+144 x^6+\frac{99 x^5}{5}-\frac{425 x^4}{4}-\frac{154 x^3}{3}+26 x^2+24 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

24*x + 26*x^2 - (154*x^3)/3 - (425*x^4)/4 + (99*x^5)/5 + 144*x^6 + (540*x^7)/7

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Maple [A]  time = 0.002, size = 35, normalized size = 0.8 \begin{align*} 24\,x+26\,{x}^{2}-{\frac{154\,{x}^{3}}{3}}-{\frac{425\,{x}^{4}}{4}}+{\frac{99\,{x}^{5}}{5}}+144\,{x}^{6}+{\frac{540\,{x}^{7}}{7}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

24*x+26*x^2-154/3*x^3-425/4*x^4+99/5*x^5+144*x^6+540/7*x^7

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Maxima [A]  time = 1.04608, size = 46, normalized size = 1.1 \begin{align*} \frac{540}{7} \, x^{7} + 144 \, x^{6} + \frac{99}{5} \, x^{5} - \frac{425}{4} \, x^{4} - \frac{154}{3} \, x^{3} + 26 \, x^{2} + 24 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

540/7*x^7 + 144*x^6 + 99/5*x^5 - 425/4*x^4 - 154/3*x^3 + 26*x^2 + 24*x

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Fricas [A]  time = 1.3733, size = 97, normalized size = 2.31 \begin{align*} \frac{540}{7} x^{7} + 144 x^{6} + \frac{99}{5} x^{5} - \frac{425}{4} x^{4} - \frac{154}{3} x^{3} + 26 x^{2} + 24 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

540/7*x^7 + 144*x^6 + 99/5*x^5 - 425/4*x^4 - 154/3*x^3 + 26*x^2 + 24*x

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Sympy [A]  time = 0.061785, size = 39, normalized size = 0.93 \begin{align*} \frac{540 x^{7}}{7} + 144 x^{6} + \frac{99 x^{5}}{5} - \frac{425 x^{4}}{4} - \frac{154 x^{3}}{3} + 26 x^{2} + 24 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

540*x**7/7 + 144*x**6 + 99*x**5/5 - 425*x**4/4 - 154*x**3/3 + 26*x**2 + 24*x

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Giac [A]  time = 2.22988, size = 46, normalized size = 1.1 \begin{align*} \frac{540}{7} \, x^{7} + 144 \, x^{6} + \frac{99}{5} \, x^{5} - \frac{425}{4} \, x^{4} - \frac{154}{3} \, x^{3} + 26 \, x^{2} + 24 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

540/7*x^7 + 144*x^6 + 99/5*x^5 - 425/4*x^4 - 154/3*x^3 + 26*x^2 + 24*x