3.1143 \(\int (1-2 x) (2+3 x)^8 (3+5 x) \, dx\)

Optimal. Leaf size=34 \[ -\frac{10}{297} (3 x+2)^{11}+\frac{37}{270} (3 x+2)^{10}-\frac{7}{243} (3 x+2)^9 \]

[Out]

(-7*(2 + 3*x)^9)/243 + (37*(2 + 3*x)^10)/270 - (10*(2 + 3*x)^11)/297

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Rubi [A]  time = 0.0232042, antiderivative size = 34, normalized size of antiderivative = 1., 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} \[ -\frac{10}{297} (3 x+2)^{11}+\frac{37}{270} (3 x+2)^{10}-\frac{7}{243} (3 x+2)^9 \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x),x]

[Out]

(-7*(2 + 3*x)^9)/243 + (37*(2 + 3*x)^10)/270 - (10*(2 + 3*x)^11)/297

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)^8 (3+5 x) \, dx &=\int \left (-\frac{7}{9} (2+3 x)^8+\frac{37}{9} (2+3 x)^9-\frac{10}{9} (2+3 x)^{10}\right ) \, dx\\ &=-\frac{7}{243} (2+3 x)^9+\frac{37}{270} (2+3 x)^{10}-\frac{10}{297} (2+3 x)^{11}\\ \end{align*}

Mathematica [A]  time = 0.0027981, size = 62, normalized size = 1.82 \[ -\frac{65610 x^{11}}{11}-\frac{356481 x^{10}}{10}-92421 x^9-133164 x^8-110160 x^7-41328 x^6+\frac{62496 x^5}{5}+24576 x^4+\frac{42752 x^3}{3}+4480 x^2+768 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x),x]

[Out]

768*x + 4480*x^2 + (42752*x^3)/3 + 24576*x^4 + (62496*x^5)/5 - 41328*x^6 - 110160*x^7 - 133164*x^8 - 92421*x^9
- (356481*x^10)/10 - (65610*x^11)/11

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Maple [A]  time = 0.001, size = 55, normalized size = 1.6 \begin{align*} -{\frac{65610\,{x}^{11}}{11}}-{\frac{356481\,{x}^{10}}{10}}-92421\,{x}^{9}-133164\,{x}^{8}-110160\,{x}^{7}-41328\,{x}^{6}+{\frac{62496\,{x}^{5}}{5}}+24576\,{x}^{4}+{\frac{42752\,{x}^{3}}{3}}+4480\,{x}^{2}+768\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)*(2+3*x)^8*(3+5*x),x)

[Out]

-65610/11*x^11-356481/10*x^10-92421*x^9-133164*x^8-110160*x^7-41328*x^6+62496/5*x^5+24576*x^4+42752/3*x^3+4480
*x^2+768*x

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Maxima [A]  time = 1.22574, size = 73, normalized size = 2.15 \begin{align*} -\frac{65610}{11} \, x^{11} - \frac{356481}{10} \, x^{10} - 92421 \, x^{9} - 133164 \, x^{8} - 110160 \, x^{7} - 41328 \, x^{6} + \frac{62496}{5} \, x^{5} + 24576 \, x^{4} + \frac{42752}{3} \, x^{3} + 4480 \, x^{2} + 768 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)^8*(3+5*x),x, algorithm="maxima")

[Out]

-65610/11*x^11 - 356481/10*x^10 - 92421*x^9 - 133164*x^8 - 110160*x^7 - 41328*x^6 + 62496/5*x^5 + 24576*x^4 +
42752/3*x^3 + 4480*x^2 + 768*x

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Fricas [A]  time = 1.33085, size = 192, normalized size = 5.65 \begin{align*} -\frac{65610}{11} x^{11} - \frac{356481}{10} x^{10} - 92421 x^{9} - 133164 x^{8} - 110160 x^{7} - 41328 x^{6} + \frac{62496}{5} x^{5} + 24576 x^{4} + \frac{42752}{3} x^{3} + 4480 x^{2} + 768 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)^8*(3+5*x),x, algorithm="fricas")

[Out]

-65610/11*x^11 - 356481/10*x^10 - 92421*x^9 - 133164*x^8 - 110160*x^7 - 41328*x^6 + 62496/5*x^5 + 24576*x^4 +
42752/3*x^3 + 4480*x^2 + 768*x

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Sympy [B]  time = 0.068013, size = 60, normalized size = 1.76 \begin{align*} - \frac{65610 x^{11}}{11} - \frac{356481 x^{10}}{10} - 92421 x^{9} - 133164 x^{8} - 110160 x^{7} - 41328 x^{6} + \frac{62496 x^{5}}{5} + 24576 x^{4} + \frac{42752 x^{3}}{3} + 4480 x^{2} + 768 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)**8*(3+5*x),x)

[Out]

-65610*x**11/11 - 356481*x**10/10 - 92421*x**9 - 133164*x**8 - 110160*x**7 - 41328*x**6 + 62496*x**5/5 + 24576
*x**4 + 42752*x**3/3 + 4480*x**2 + 768*x

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Giac [A]  time = 3.69596, size = 73, normalized size = 2.15 \begin{align*} -\frac{65610}{11} \, x^{11} - \frac{356481}{10} \, x^{10} - 92421 \, x^{9} - 133164 \, x^{8} - 110160 \, x^{7} - 41328 \, x^{6} + \frac{62496}{5} \, x^{5} + 24576 \, x^{4} + \frac{42752}{3} \, x^{3} + 4480 \, x^{2} + 768 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)^8*(3+5*x),x, algorithm="giac")

[Out]

-65610/11*x^11 - 356481/10*x^10 - 92421*x^9 - 133164*x^8 - 110160*x^7 - 41328*x^6 + 62496/5*x^5 + 24576*x^4 +
42752/3*x^3 + 4480*x^2 + 768*x