3.1177 \(\int (1-2 x) (2+3 x)^6 (3+5 x)^3 \, dx\)

Optimal. Leaf size=56 \[ -\frac{250 (3 x+2)^{11}}{2673}+\frac{205}{486} (3 x+2)^{10}-\frac{185}{729} (3 x+2)^9+\frac{107 (3 x+2)^8}{1944}-\frac{1}{243} (3 x+2)^7 \]

[Out]

-(2 + 3*x)^7/243 + (107*(2 + 3*x)^8)/1944 - (185*(2 + 3*x)^9)/729 + (205*(2 + 3*x)^10)/486 - (250*(2 + 3*x)^11
)/2673

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Rubi [A]  time = 0.0288724, 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} \[ -\frac{250 (3 x+2)^{11}}{2673}+\frac{205}{486} (3 x+2)^{10}-\frac{185}{729} (3 x+2)^9+\frac{107 (3 x+2)^8}{1944}-\frac{1}{243} (3 x+2)^7 \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)*(2 + 3*x)^6*(3 + 5*x)^3,x]

[Out]

-(2 + 3*x)^7/243 + (107*(2 + 3*x)^8)/1944 - (185*(2 + 3*x)^9)/729 + (205*(2 + 3*x)^10)/486 - (250*(2 + 3*x)^11
)/2673

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)^6 (3+5 x)^3 \, dx &=\int \left (-\frac{7}{81} (2+3 x)^6+\frac{107}{81} (2+3 x)^7-\frac{185}{27} (2+3 x)^8+\frac{1025}{81} (2+3 x)^9-\frac{250}{81} (2+3 x)^{10}\right ) \, dx\\ &=-\frac{1}{243} (2+3 x)^7+\frac{107 (2+3 x)^8}{1944}-\frac{185}{729} (2+3 x)^9+\frac{205}{486} (2+3 x)^{10}-\frac{250 (2+3 x)^{11}}{2673}\\ \end{align*}

Mathematica [A]  time = 0.0022877, size = 60, normalized size = 1.07 \[ -\frac{182250 x^{11}}{11}-\frac{193185 x^{10}}{2}-243945 x^9-\frac{2731671 x^8}{8}-272403 x^7-94668 x^6+36148 x^5+61220 x^4+34032 x^3+10368 x^2+1728 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)*(2 + 3*x)^6*(3 + 5*x)^3,x]

[Out]

1728*x + 10368*x^2 + 34032*x^3 + 61220*x^4 + 36148*x^5 - 94668*x^6 - 272403*x^7 - (2731671*x^8)/8 - 243945*x^9
- (193185*x^10)/2 - (182250*x^11)/11

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Maple [A]  time = 0.002, size = 55, normalized size = 1. \begin{align*} -{\frac{182250\,{x}^{11}}{11}}-{\frac{193185\,{x}^{10}}{2}}-243945\,{x}^{9}-{\frac{2731671\,{x}^{8}}{8}}-272403\,{x}^{7}-94668\,{x}^{6}+36148\,{x}^{5}+61220\,{x}^{4}+34032\,{x}^{3}+10368\,{x}^{2}+1728\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)*(2+3*x)^6*(3+5*x)^3,x)

[Out]

-182250/11*x^11-193185/2*x^10-243945*x^9-2731671/8*x^8-272403*x^7-94668*x^6+36148*x^5+61220*x^4+34032*x^3+1036
8*x^2+1728*x

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Maxima [A]  time = 1.08598, size = 73, normalized size = 1.3 \begin{align*} -\frac{182250}{11} \, x^{11} - \frac{193185}{2} \, x^{10} - 243945 \, x^{9} - \frac{2731671}{8} \, x^{8} - 272403 \, x^{7} - 94668 \, x^{6} + 36148 \, x^{5} + 61220 \, x^{4} + 34032 \, x^{3} + 10368 \, x^{2} + 1728 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)^6*(3+5*x)^3,x, algorithm="maxima")

[Out]

-182250/11*x^11 - 193185/2*x^10 - 243945*x^9 - 2731671/8*x^8 - 272403*x^7 - 94668*x^6 + 36148*x^5 + 61220*x^4
+ 34032*x^3 + 10368*x^2 + 1728*x

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Fricas [A]  time = 1.53929, size = 194, normalized size = 3.46 \begin{align*} -\frac{182250}{11} x^{11} - \frac{193185}{2} x^{10} - 243945 x^{9} - \frac{2731671}{8} x^{8} - 272403 x^{7} - 94668 x^{6} + 36148 x^{5} + 61220 x^{4} + 34032 x^{3} + 10368 x^{2} + 1728 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)^6*(3+5*x)^3,x, algorithm="fricas")

[Out]

-182250/11*x^11 - 193185/2*x^10 - 243945*x^9 - 2731671/8*x^8 - 272403*x^7 - 94668*x^6 + 36148*x^5 + 61220*x^4
+ 34032*x^3 + 10368*x^2 + 1728*x

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Sympy [A]  time = 0.070004, size = 58, normalized size = 1.04 \begin{align*} - \frac{182250 x^{11}}{11} - \frac{193185 x^{10}}{2} - 243945 x^{9} - \frac{2731671 x^{8}}{8} - 272403 x^{7} - 94668 x^{6} + 36148 x^{5} + 61220 x^{4} + 34032 x^{3} + 10368 x^{2} + 1728 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)**6*(3+5*x)**3,x)

[Out]

-182250*x**11/11 - 193185*x**10/2 - 243945*x**9 - 2731671*x**8/8 - 272403*x**7 - 94668*x**6 + 36148*x**5 + 612
20*x**4 + 34032*x**3 + 10368*x**2 + 1728*x

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Giac [A]  time = 2.77752, size = 73, normalized size = 1.3 \begin{align*} -\frac{182250}{11} \, x^{11} - \frac{193185}{2} \, x^{10} - 243945 \, x^{9} - \frac{2731671}{8} \, x^{8} - 272403 \, x^{7} - 94668 \, x^{6} + 36148 \, x^{5} + 61220 \, x^{4} + 34032 \, x^{3} + 10368 \, x^{2} + 1728 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)*(2+3*x)^6*(3+5*x)^3,x, algorithm="giac")

[Out]

-182250/11*x^11 - 193185/2*x^10 - 243945*x^9 - 2731671/8*x^8 - 272403*x^7 - 94668*x^6 + 36148*x^5 + 61220*x^4
+ 34032*x^3 + 10368*x^2 + 1728*x