\(\int (1-2 x)^2 (2+3 x)^8 (3+5 x)^2 \, dx\) [1253]

Optimal result

Integrand size = 22, antiderivative size = 56 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x)^2 \, dx=\frac {49 (2+3 x)^9}{2187}-\frac {259 (2+3 x)^{10}}{1215}+\frac {503}{891} (2+3 x)^{11}-\frac {185}{729} (2+3 x)^{12}+\frac {100 (2+3 x)^{13}}{3159} \]

[Out]

49/2187*(2+3*x)^9-259/1215*(2+3*x)^10+503/891*(2+3*x)^11-185/729*(2+3*x)^12+100/3159*(2+3*x)^13

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, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x)^2 \, dx=\frac {100 (3 x+2)^{13}}{3159}-\frac {185}{729} (3 x+2)^{12}+\frac {503}{891} (3 x+2)^{11}-\frac {259 (3 x+2)^{10}}{1215}+\frac {49 (3 x+2)^9}{2187} \]

[In]

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

[Out]

(49*(2 + 3*x)^9)/2187 - (259*(2 + 3*x)^10)/1215 + (503*(2 + 3*x)^11)/891 - (185*(2 + 3*x)^12)/729 + (100*(2 +
3*x)^13)/3159

Rule 90

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandI
ntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] &&
(IntegerQ[p] || (GtQ[m, 0] && GeQ[n, -1]))

Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {49}{81} (2+3 x)^8-\frac {518}{81} (2+3 x)^9+\frac {503}{27} (2+3 x)^{10}-\frac {740}{81} (2+3 x)^{11}+\frac {100}{81} (2+3 x)^{12}\right ) \, dx \\ & = \frac {49 (2+3 x)^9}{2187}-\frac {259 (2+3 x)^{10}}{1215}+\frac {503}{891} (2+3 x)^{11}-\frac {185}{729} (2+3 x)^{12}+\frac {100 (2+3 x)^{13}}{3159} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 74, normalized size of antiderivative = 1.32 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x)^2 \, dx=2304 x+13056 x^2+\frac {111616 x^3}{3}+40640 x^4-\frac {338336 x^5}{5}-298240 x^6-384336 x^7+6858 x^8+697905 x^9+\frac {5207733 x^{10}}{5}+\frac {8477541 x^{11}}{11}+302535 x^{12}+\frac {656100 x^{13}}{13} \]

[In]

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

[Out]

2304*x + 13056*x^2 + (111616*x^3)/3 + 40640*x^4 - (338336*x^5)/5 - 298240*x^6 - 384336*x^7 + 6858*x^8 + 697905
*x^9 + (5207733*x^10)/5 + (8477541*x^11)/11 + 302535*x^12 + (656100*x^13)/13

Maple [A] (verified)

Time = 2.26 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.14

method	result	size
gosper	\(\frac {x \left (108256500 x^{12}[phone] x^{11}[phone] x^{10}[phone] x^{9}[phone] x^{8}[phone] x^{7}-824400720 x^{6}-639724800 x^{5}-145146144 x^{4}[phone] x^{3}[phone] x^{2}[phone] x +4942080\right )}{2145}\)	\(64\)
default	\(\frac {656100}{13} x^{13}+302535 x^{12}+\frac {8477541}{11} x^{11}+\frac {5207733}{5} x^{10}+697905 x^{9}+6858 x^{8}-384336 x^{7}-298240 x^{6}-\frac {338336}{5} x^{5}+40640 x^{4}+\frac {111616}{3} x^{3}+13056 x^{2}+2304 x\)	\(65\)
norman	\(\frac {656100}{13} x^{13}+302535 x^{12}+\frac {8477541}{11} x^{11}+\frac {5207733}{5} x^{10}+697905 x^{9}+6858 x^{8}-384336 x^{7}-298240 x^{6}-\frac {338336}{5} x^{5}+40640 x^{4}+\frac {111616}{3} x^{3}+13056 x^{2}+2304 x\)	\(65\)
risch	\(\frac {656100}{13} x^{13}+302535 x^{12}+\frac {8477541}{11} x^{11}+\frac {5207733}{5} x^{10}+697905 x^{9}+6858 x^{8}-384336 x^{7}-298240 x^{6}-\frac {338336}{5} x^{5}+40640 x^{4}+\frac {111616}{3} x^{3}+13056 x^{2}+2304 x\)	\(65\)
parallelrisch	\(\frac {656100}{13} x^{13}+302535 x^{12}+\frac {8477541}{11} x^{11}+\frac {5207733}{5} x^{10}+697905 x^{9}+6858 x^{8}-384336 x^{7}-298240 x^{6}-\frac {338336}{5} x^{5}+40640 x^{4}+\frac {111616}{3} x^{3}+13056 x^{2}+2304 x\)	\(65\)

[In]

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

[Out]

1/2145*x*(108256500*x^12+648937575*x^11+1653120495*x^10+2234117457*x^9+1497006225*x^8+14710410*x^7-824400720*x
^6-639724800*x^5-145146144*x^4+87172800*x^3+79805440*x^2+28005120*x+4942080)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.14 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x)^2 \, dx=\frac {656100}{13} \, x^{13} + 302535 \, x^{12} + \frac {8477541}{11} \, x^{11} + \frac {5207733}{5} \, x^{10} + 697905 \, x^{9} + 6858 \, x^{8} - 384336 \, x^{7} - 298240 \, x^{6} - \frac {338336}{5} \, x^{5} + 40640 \, x^{4} + \frac {111616}{3} \, x^{3} + 13056 \, x^{2} + 2304 \, x \]

[In]

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

[Out]

656100/13*x^13 + 302535*x^12 + 8477541/11*x^11 + 5207733/5*x^10 + 697905*x^9 + 6858*x^8 - 384336*x^7 - 298240*
x^6 - 338336/5*x^5 + 40640*x^4 + 111616/3*x^3 + 13056*x^2 + 2304*x

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 71, normalized size of antiderivative = 1.27 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x)^2 \, dx=\frac {656100 x^{13}}{13} + 302535 x^{12} + \frac {8477541 x^{11}}{11} + \frac {5207733 x^{10}}{5} + 697905 x^{9} + 6858 x^{8} - 384336 x^{7} - 298240 x^{6} - \frac {338336 x^{5}}{5} + 40640 x^{4} + \frac {111616 x^{3}}{3} + 13056 x^{2} + 2304 x \]

[In]

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

[Out]

656100*x**13/13 + 302535*x**12 + 8477541*x**11/11 + 5207733*x**10/5 + 697905*x**9 + 6858*x**8 - 384336*x**7 -
298240*x**6 - 338336*x**5/5 + 40640*x**4 + 111616*x**3/3 + 13056*x**2 + 2304*x

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.14 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x)^2 \, dx=\frac {656100}{13} \, x^{13} + 302535 \, x^{12} + \frac {8477541}{11} \, x^{11} + \frac {5207733}{5} \, x^{10} + 697905 \, x^{9} + 6858 \, x^{8} - 384336 \, x^{7} - 298240 \, x^{6} - \frac {338336}{5} \, x^{5} + 40640 \, x^{4} + \frac {111616}{3} \, x^{3} + 13056 \, x^{2} + 2304 \, x \]

[In]

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

[Out]

656100/13*x^13 + 302535*x^12 + 8477541/11*x^11 + 5207733/5*x^10 + 697905*x^9 + 6858*x^8 - 384336*x^7 - 298240*
x^6 - 338336/5*x^5 + 40640*x^4 + 111616/3*x^3 + 13056*x^2 + 2304*x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.14 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x)^2 \, dx=\frac {656100}{13} \, x^{13} + 302535 \, x^{12} + \frac {8477541}{11} \, x^{11} + \frac {5207733}{5} \, x^{10} + 697905 \, x^{9} + 6858 \, x^{8} - 384336 \, x^{7} - 298240 \, x^{6} - \frac {338336}{5} \, x^{5} + 40640 \, x^{4} + \frac {111616}{3} \, x^{3} + 13056 \, x^{2} + 2304 \, x \]

[In]

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

[Out]

656100/13*x^13 + 302535*x^12 + 8477541/11*x^11 + 5207733/5*x^10 + 697905*x^9 + 6858*x^8 - 384336*x^7 - 298240*
x^6 - 338336/5*x^5 + 40640*x^4 + 111616/3*x^3 + 13056*x^2 + 2304*x

Mupad [B] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.14 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x)^2 \, dx=\frac {656100\,x^{13}}{13}+302535\,x^{12}+\frac {8477541\,x^{11}}{11}+\frac {5207733\,x^{10}}{5}+697905\,x^9+6858\,x^8-384336\,x^7-298240\,x^6-\frac {338336\,x^5}{5}+40640\,x^4+\frac {111616\,x^3}{3}+13056\,x^2+2304\,x \]

[In]

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

[Out]

2304*x + 13056*x^2 + (111616*x^3)/3 + 40640*x^4 - (338336*x^5)/5 - 298240*x^6 - 384336*x^7 + 6858*x^8 + 697905
*x^9 + (5207733*x^10)/5 + (8477541*x^11)/11 + 302535*x^12 + (656100*x^13)/13