3.1362 \(\int (1-2 x)^3 (2+3 x) (3+5 x)^2 \, dx\)

Optimal. Leaf size=46 \[ -\frac{600 x^7}{7}-\frac{110 x^6}{3}+\frac{534 x^5}{5}+\frac{135 x^4}{4}-\frac{166 x^3}{3}-\frac{21 x^2}{2}+18 x \]

[Out]

18*x - (21*x^2)/2 - (166*x^3)/3 + (135*x^4)/4 + (534*x^5)/5 - (110*x^6)/3 - (600*x^7)/7

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Rubi [A]  time = 0.01598, antiderivative size = 46, 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} \[ -\frac{600 x^7}{7}-\frac{110 x^6}{3}+\frac{534 x^5}{5}+\frac{135 x^4}{4}-\frac{166 x^3}{3}-\frac{21 x^2}{2}+18 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

18*x - (21*x^2)/2 - (166*x^3)/3 + (135*x^4)/4 + (534*x^5)/5 - (110*x^6)/3 - (600*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)^3 (2+3 x) (3+5 x)^2 \, dx &=\int \left (18-21 x-166 x^2+135 x^3+534 x^4-220 x^5-600 x^6\right ) \, dx\\ &=18 x-\frac{21 x^2}{2}-\frac{166 x^3}{3}+\frac{135 x^4}{4}+\frac{534 x^5}{5}-\frac{110 x^6}{3}-\frac{600 x^7}{7}\\ \end{align*}

Mathematica [A]  time = 0.0008486, size = 46, normalized size = 1. \[ -\frac{600 x^7}{7}-\frac{110 x^6}{3}+\frac{534 x^5}{5}+\frac{135 x^4}{4}-\frac{166 x^3}{3}-\frac{21 x^2}{2}+18 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

18*x - (21*x^2)/2 - (166*x^3)/3 + (135*x^4)/4 + (534*x^5)/5 - (110*x^6)/3 - (600*x^7)/7

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Maple [A]  time = 0.001, size = 35, normalized size = 0.8 \begin{align*} 18\,x-{\frac{21\,{x}^{2}}{2}}-{\frac{166\,{x}^{3}}{3}}+{\frac{135\,{x}^{4}}{4}}+{\frac{534\,{x}^{5}}{5}}-{\frac{110\,{x}^{6}}{3}}-{\frac{600\,{x}^{7}}{7}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

18*x-21/2*x^2-166/3*x^3+135/4*x^4+534/5*x^5-110/3*x^6-600/7*x^7

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Maxima [A]  time = 1.02157, size = 46, normalized size = 1. \begin{align*} -\frac{600}{7} \, x^{7} - \frac{110}{3} \, x^{6} + \frac{534}{5} \, x^{5} + \frac{135}{4} \, x^{4} - \frac{166}{3} \, x^{3} - \frac{21}{2} \, x^{2} + 18 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-600/7*x^7 - 110/3*x^6 + 534/5*x^5 + 135/4*x^4 - 166/3*x^3 - 21/2*x^2 + 18*x

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Fricas [A]  time = 1.14342, size = 105, normalized size = 2.28 \begin{align*} -\frac{600}{7} x^{7} - \frac{110}{3} x^{6} + \frac{534}{5} x^{5} + \frac{135}{4} x^{4} - \frac{166}{3} x^{3} - \frac{21}{2} x^{2} + 18 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-600/7*x^7 - 110/3*x^6 + 534/5*x^5 + 135/4*x^4 - 166/3*x^3 - 21/2*x^2 + 18*x

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Sympy [A]  time = 0.060589, size = 42, normalized size = 0.91 \begin{align*} - \frac{600 x^{7}}{7} - \frac{110 x^{6}}{3} + \frac{534 x^{5}}{5} + \frac{135 x^{4}}{4} - \frac{166 x^{3}}{3} - \frac{21 x^{2}}{2} + 18 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-600*x**7/7 - 110*x**6/3 + 534*x**5/5 + 135*x**4/4 - 166*x**3/3 - 21*x**2/2 + 18*x

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Giac [A]  time = 2.63564, size = 46, normalized size = 1. \begin{align*} -\frac{600}{7} \, x^{7} - \frac{110}{3} \, x^{6} + \frac{534}{5} \, x^{5} + \frac{135}{4} \, x^{4} - \frac{166}{3} \, x^{3} - \frac{21}{2} \, x^{2} + 18 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-600/7*x^7 - 110/3*x^6 + 534/5*x^5 + 135/4*x^4 - 166/3*x^3 - 21/2*x^2 + 18*x