3.1342 \(\int (1-2 x)^3 (2+3 x)^4 (3+5 x) \, dx\)

Optimal. Leaf size=56 \[ -\frac{40 (3 x+2)^9}{2187}+\frac{107}{486} (3 x+2)^8-\frac{74}{81} (3 x+2)^7+\frac{2009 (3 x+2)^6}{1458}-\frac{343 (3 x+2)^5}{1215} \]

[Out]

(-343*(2 + 3*x)^5)/1215 + (2009*(2 + 3*x)^6)/1458 - (74*(2 + 3*x)^7)/81 + (107*(2 + 3*x)^8)/486 - (40*(2 + 3*x
)^9)/2187

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Rubi [A]  time = 0.0225159, antiderivative size = 56, 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} \[ -\frac{40 (3 x+2)^9}{2187}+\frac{107}{486} (3 x+2)^8-\frac{74}{81} (3 x+2)^7+\frac{2009 (3 x+2)^6}{1458}-\frac{343 (3 x+2)^5}{1215} \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x),x]

[Out]

(-343*(2 + 3*x)^5)/1215 + (2009*(2 + 3*x)^6)/1458 - (74*(2 + 3*x)^7)/81 + (107*(2 + 3*x)^8)/486 - (40*(2 + 3*x
)^9)/2187

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)^4 (3+5 x) \, dx &=\int \left (-\frac{343}{81} (2+3 x)^4+\frac{2009}{81} (2+3 x)^5-\frac{518}{27} (2+3 x)^6+\frac{428}{81} (2+3 x)^7-\frac{40}{81} (2+3 x)^8\right ) \, dx\\ &=-\frac{343 (2+3 x)^5}{1215}+\frac{2009 (2+3 x)^6}{1458}-\frac{74}{81} (2+3 x)^7+\frac{107}{486} (2+3 x)^8-\frac{40 (2+3 x)^9}{2187}\\ \end{align*}

Mathematica [A]  time = 0.001982, size = 50, normalized size = 0.89 \[ -360 x^9-\frac{1431 x^8}{2}-54 x^7+\frac{1393 x^6}{2}+\frac{1547 x^5}{5}-252 x^4-168 x^3+40 x^2+48 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x),x]

[Out]

48*x + 40*x^2 - 168*x^3 - 252*x^4 + (1547*x^5)/5 + (1393*x^6)/2 - 54*x^7 - (1431*x^8)/2 - 360*x^9

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Maple [A]  time = 0.001, size = 45, normalized size = 0.8 \begin{align*} -360\,{x}^{9}-{\frac{1431\,{x}^{8}}{2}}-54\,{x}^{7}+{\frac{1393\,{x}^{6}}{2}}+{\frac{1547\,{x}^{5}}{5}}-252\,{x}^{4}-168\,{x}^{3}+40\,{x}^{2}+48\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^3*(2+3*x)^4*(3+5*x),x)

[Out]

-360*x^9-1431/2*x^8-54*x^7+1393/2*x^6+1547/5*x^5-252*x^4-168*x^3+40*x^2+48*x

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Maxima [A]  time = 1.20624, size = 59, normalized size = 1.05 \begin{align*} -360 \, x^{9} - \frac{1431}{2} \, x^{8} - 54 \, x^{7} + \frac{1393}{2} \, x^{6} + \frac{1547}{5} \, x^{5} - 252 \, x^{4} - 168 \, x^{3} + 40 \, x^{2} + 48 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^4*(3+5*x),x, algorithm="maxima")

[Out]

-360*x^9 - 1431/2*x^8 - 54*x^7 + 1393/2*x^6 + 1547/5*x^5 - 252*x^4 - 168*x^3 + 40*x^2 + 48*x

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Fricas [A]  time = 1.07901, size = 127, normalized size = 2.27 \begin{align*} -360 x^{9} - \frac{1431}{2} x^{8} - 54 x^{7} + \frac{1393}{2} x^{6} + \frac{1547}{5} x^{5} - 252 x^{4} - 168 x^{3} + 40 x^{2} + 48 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^4*(3+5*x),x, algorithm="fricas")

[Out]

-360*x^9 - 1431/2*x^8 - 54*x^7 + 1393/2*x^6 + 1547/5*x^5 - 252*x^4 - 168*x^3 + 40*x^2 + 48*x

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Sympy [A]  time = 0.064435, size = 48, normalized size = 0.86 \begin{align*} - 360 x^{9} - \frac{1431 x^{8}}{2} - 54 x^{7} + \frac{1393 x^{6}}{2} + \frac{1547 x^{5}}{5} - 252 x^{4} - 168 x^{3} + 40 x^{2} + 48 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**3*(2+3*x)**4*(3+5*x),x)

[Out]

-360*x**9 - 1431*x**8/2 - 54*x**7 + 1393*x**6/2 + 1547*x**5/5 - 252*x**4 - 168*x**3 + 40*x**2 + 48*x

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Giac [A]  time = 3.07132, size = 59, normalized size = 1.05 \begin{align*} -360 \, x^{9} - \frac{1431}{2} \, x^{8} - 54 \, x^{7} + \frac{1393}{2} \, x^{6} + \frac{1547}{5} \, x^{5} - 252 \, x^{4} - 168 \, x^{3} + 40 \, x^{2} + 48 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^4*(3+5*x),x, algorithm="giac")

[Out]

-360*x^9 - 1431/2*x^8 - 54*x^7 + 1393/2*x^6 + 1547/5*x^5 - 252*x^4 - 168*x^3 + 40*x^2 + 48*x