\(\int (1-2 x)^3 (2+3 x)^7 (3+5 x) \, dx\) [1339]

Optimal result

Integrand size = 20, antiderivative size = 56 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x) \, dx=-\frac {343 (2+3 x)^8}{1944}+\frac {2009 (2+3 x)^9}{2187}-\frac {259}{405} (2+3 x)^{10}+\frac {428 (2+3 x)^{11}}{2673}-\frac {10}{729} (2+3 x)^{12} \]

[Out]

-343/1944*(2+3*x)^8+2009/2187*(2+3*x)^9-259/405*(2+3*x)^10+428/2673*(2+3*x)^11-10/729*(2+3*x)^12

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x) \, dx=-\frac {10}{729} (3 x+2)^{12}+\frac {428 (3 x+2)^{11}}{2673}-\frac {259}{405} (3 x+2)^{10}+\frac {2009 (3 x+2)^9}{2187}-\frac {343 (3 x+2)^8}{1944} \]

[In]

Int[(1 - 2*x)^3*(2 + 3*x)^7*(3 + 5*x),x]

[Out]

(-343*(2 + 3*x)^8)/1944 + (2009*(2 + 3*x)^9)/2187 - (259*(2 + 3*x)^10)/405 + (428*(2 + 3*x)^11)/2673 - (10*(2
+ 3*x)^12)/729

Rule 78

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*} \text {integral}& = \int \left (-\frac {343}{81} (2+3 x)^7+\frac {2009}{81} (2+3 x)^8-\frac {518}{27} (2+3 x)^9+\frac {428}{81} (2+3 x)^{10}-\frac {40}{81} (2+3 x)^{11}\right ) \, dx \\ & = -\frac {343 (2+3 x)^8}{1944}+\frac {2009 (2+3 x)^9}{2187}-\frac {259}{405} (2+3 x)^{10}+\frac {428 (2+3 x)^{11}}{2673}-\frac {10}{729} (2+3 x)^{12} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 67, normalized size of antiderivative = 1.20 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x) \, dx=384 x+1184 x^2+480 x^3-5148 x^4-\frac {48968 x^5}{5}+3514 x^6+29106 x^7+\frac {208035 x^8}{8}-15507 x^9-\frac {217971 x^{10}}{5}-\frac {329508 x^{11}}{11}-7290 x^{12} \]

[In]

Integrate[(1 - 2*x)^3*(2 + 3*x)^7*(3 + 5*x),x]

[Out]

384*x + 1184*x^2 + 480*x^3 - 5148*x^4 - (48968*x^5)/5 + 3514*x^6 + 29106*x^7 + (208035*x^8)/8 - 15507*x^9 - (2
17971*x^10)/5 - (329508*x^11)/11 - 7290*x^12

Maple [A] (verified)

Time = 2.36 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.05

method	result	size
gosper	\(-\frac {x \left (3207600 x^{11}[phone] x^{10}[phone] x^{9}+6823080 x^{8}-11441925 x^{7}-12806640 x^{6}-1546160 x^{5}+4309184 x^{4}+2265120 x^{3}-211200 x^{2}-520960 x -168960\right )}{440}\)	\(59\)
default	\(-7290 x^{12}-\frac {329508}{11} x^{11}-\frac {217971}{5} x^{10}-15507 x^{9}+\frac {208035}{8} x^{8}+29106 x^{7}+3514 x^{6}-\frac {48968}{5} x^{5}-5148 x^{4}+480 x^{3}+1184 x^{2}+384 x\)	\(60\)
norman	\(-7290 x^{12}-\frac {329508}{11} x^{11}-\frac {217971}{5} x^{10}-15507 x^{9}+\frac {208035}{8} x^{8}+29106 x^{7}+3514 x^{6}-\frac {48968}{5} x^{5}-5148 x^{4}+480 x^{3}+1184 x^{2}+384 x\)	\(60\)
risch	\(-7290 x^{12}-\frac {329508}{11} x^{11}-\frac {217971}{5} x^{10}-15507 x^{9}+\frac {208035}{8} x^{8}+29106 x^{7}+3514 x^{6}-\frac {48968}{5} x^{5}-5148 x^{4}+480 x^{3}+1184 x^{2}+384 x\)	\(60\)
parallelrisch	\(-7290 x^{12}-\frac {329508}{11} x^{11}-\frac {217971}{5} x^{10}-15507 x^{9}+\frac {208035}{8} x^{8}+29106 x^{7}+3514 x^{6}-\frac {48968}{5} x^{5}-5148 x^{4}+480 x^{3}+1184 x^{2}+384 x\)	\(60\)

[In]

int((1-2*x)^3*(2+3*x)^7*(3+5*x),x,method=_RETURNVERBOSE)

[Out]

-1/440*x*(3207600*x^11+13180320*x^10+19181448*x^9+6823080*x^8-11441925*x^7-12806640*x^6-1546160*x^5+4309184*x^
4+2265120*x^3-211200*x^2-520960*x-168960)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.05 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x) \, dx=-7290 \, x^{12} - \frac {329508}{11} \, x^{11} - \frac {217971}{5} \, x^{10} - 15507 \, x^{9} + \frac {208035}{8} \, x^{8} + 29106 \, x^{7} + 3514 \, x^{6} - \frac {48968}{5} \, x^{5} - 5148 \, x^{4} + 480 \, x^{3} + 1184 \, x^{2} + 384 \, x \]

[In]

integrate((1-2*x)^3*(2+3*x)^7*(3+5*x),x, algorithm="fricas")

[Out]

-7290*x^12 - 329508/11*x^11 - 217971/5*x^10 - 15507*x^9 + 208035/8*x^8 + 29106*x^7 + 3514*x^6 - 48968/5*x^5 -
5148*x^4 + 480*x^3 + 1184*x^2 + 384*x

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 65, normalized size of antiderivative = 1.16 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x) \, dx=- 7290 x^{12} - \frac {329508 x^{11}}{11} - \frac {217971 x^{10}}{5} - 15507 x^{9} + \frac {208035 x^{8}}{8} + 29106 x^{7} + 3514 x^{6} - \frac {48968 x^{5}}{5} - 5148 x^{4} + 480 x^{3} + 1184 x^{2} + 384 x \]

[In]

integrate((1-2*x)**3*(2+3*x)**7*(3+5*x),x)

[Out]

-7290*x**12 - 329508*x**11/11 - 217971*x**10/5 - 15507*x**9 + 208035*x**8/8 + 29106*x**7 + 3514*x**6 - 48968*x
**5/5 - 5148*x**4 + 480*x**3 + 1184*x**2 + 384*x

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.05 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x) \, dx=-7290 \, x^{12} - \frac {329508}{11} \, x^{11} - \frac {217971}{5} \, x^{10} - 15507 \, x^{9} + \frac {208035}{8} \, x^{8} + 29106 \, x^{7} + 3514 \, x^{6} - \frac {48968}{5} \, x^{5} - 5148 \, x^{4} + 480 \, x^{3} + 1184 \, x^{2} + 384 \, x \]

[In]

integrate((1-2*x)^3*(2+3*x)^7*(3+5*x),x, algorithm="maxima")

[Out]

-7290*x^12 - 329508/11*x^11 - 217971/5*x^10 - 15507*x^9 + 208035/8*x^8 + 29106*x^7 + 3514*x^6 - 48968/5*x^5 -
5148*x^4 + 480*x^3 + 1184*x^2 + 384*x

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.05 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x) \, dx=-7290 \, x^{12} - \frac {329508}{11} \, x^{11} - \frac {217971}{5} \, x^{10} - 15507 \, x^{9} + \frac {208035}{8} \, x^{8} + 29106 \, x^{7} + 3514 \, x^{6} - \frac {48968}{5} \, x^{5} - 5148 \, x^{4} + 480 \, x^{3} + 1184 \, x^{2} + 384 \, x \]

[In]

integrate((1-2*x)^3*(2+3*x)^7*(3+5*x),x, algorithm="giac")

[Out]

-7290*x^12 - 329508/11*x^11 - 217971/5*x^10 - 15507*x^9 + 208035/8*x^8 + 29106*x^7 + 3514*x^6 - 48968/5*x^5 -
5148*x^4 + 480*x^3 + 1184*x^2 + 384*x

Mupad [B] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.05 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x) \, dx=-7290\,x^{12}-\frac {329508\,x^{11}}{11}-\frac {217971\,x^{10}}{5}-15507\,x^9+\frac {208035\,x^8}{8}+29106\,x^7+3514\,x^6-\frac {48968\,x^5}{5}-5148\,x^4+480\,x^3+1184\,x^2+384\,x \]

[In]

int(-(2*x - 1)^3*(3*x + 2)^7*(5*x + 3),x)

[Out]

384*x + 1184*x^2 + 480*x^3 - 5148*x^4 - (48968*x^5)/5 + 3514*x^6 + 29106*x^7 + (208035*x^8)/8 - 15507*x^9 - (2
17971*x^10)/5 - (329508*x^11)/11 - 7290*x^12