\(\int (5-2 x)^6 (2+3 x)^3 (-16+33 x) \, dx\) [1192]

Optimal result

Integrand size = 20, antiderivative size = 18 \[ \int (5-2 x)^6 (2+3 x)^3 (-16+33 x) \, dx=-\frac {1}{2} (5-2 x)^7 (2+3 x)^4 \]

[Out]

-1/2*(5-2*x)^7*(2+3*x)^4

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {75} \[ \int (5-2 x)^6 (2+3 x)^3 (-16+33 x) \, dx=-\frac {1}{2} (5-2 x)^7 (3 x+2)^4 \]

[In]

Int[(5 - 2*x)^6*(2 + 3*x)^3*(-16 + 33*x),x]

[Out]

-1/2*((5 - 2*x)^7*(2 + 3*x)^4)

Rule 75

Int[((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Simp[b*(c + d*x)^
(n + 1)*((e + f*x)^(p + 1)/(d*f*(n + p + 2))), x] /; FreeQ[{a, b, c, d, e, f, n, p}, x] && NeQ[n + p + 2, 0] &
& EqQ[a*d*f*(n + p + 2) - b*(d*e*(n + 1) + c*f*(p + 1)), 0]

Rubi steps \begin{align*} \text {integral}& = -\frac {1}{2} (5-2 x)^7 (2+3 x)^4 \\ \end{align*}

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(56\) vs. \(2(18)=36\).

Time = 0.00 (sec) , antiderivative size = 56, normalized size of antiderivative = 3.11 \[ \int (5-2 x)^6 (2+3 x)^3 (-16+33 x) \, dx=-2000000 x-37500 x^2+3987500 x^3-\frac {98125 x^4}{2}-3816225 x^5+1497230 x^6+1235404 x^7-1256376 x^8+452304 x^9-76896 x^{10}+5184 x^{11} \]

[In]

Integrate[(5 - 2*x)^6*(2 + 3*x)^3*(-16 + 33*x),x]

[Out]

-2000000*x - 37500*x^2 + 3987500*x^3 - (98125*x^4)/2 - 3816225*x^5 + 1497230*x^6 + 1235404*x^7 - 1256376*x^8 +
452304*x^9 - 76896*x^10 + 5184*x^11

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(53\) vs. \(2(16)=32\).

Time = 2.19 (sec) , antiderivative size = 54, normalized size of antiderivative = 3.00

method	result	size
gosper	\(\frac {x \left (10368 x^{10}-153792 x^{9}+904608 x^{8}-2512752 x^{7}+2470808 x^{6}+2994460 x^{5}-7632450 x^{4}-98125 x^{3}+7975000 x^{2}-75000 x -4000000\right )}{2}\)	\(54\)
default	\(5184 x^{11}-76896 x^{10}+452304 x^{9}-1256376 x^{8}+1235404 x^{7}+1497230 x^{6}-3816225 x^{5}-\frac {98125}{2} x^{4}+3987500 x^{3}-37500 x^{2}-2000000 x\)	\(55\)
norman	\(5184 x^{11}-76896 x^{10}+452304 x^{9}-1256376 x^{8}+1235404 x^{7}+1497230 x^{6}-3816225 x^{5}-\frac {98125}{2} x^{4}+3987500 x^{3}-37500 x^{2}-2000000 x\)	\(55\)
risch	\(5184 x^{11}-76896 x^{10}+452304 x^{9}-1256376 x^{8}+1235404 x^{7}+1497230 x^{6}-3816225 x^{5}-\frac {98125}{2} x^{4}+3987500 x^{3}-37500 x^{2}-2000000 x\)	\(55\)
parallelrisch	\(5184 x^{11}-76896 x^{10}+452304 x^{9}-1256376 x^{8}+1235404 x^{7}+1497230 x^{6}-3816225 x^{5}-\frac {98125}{2} x^{4}+3987500 x^{3}-37500 x^{2}-2000000 x\)	\(55\)

[In]

int((5-2*x)^6*(2+3*x)^3*(-16+33*x),x,method=_RETURNVERBOSE)

[Out]

1/2*x*(10368*x^10-153792*x^9+904608*x^8-2512752*x^7+2470808*x^6+2994460*x^5-7632450*x^4-98125*x^3+7975000*x^2-
75000*x-4000000)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (16) = 32\).

Time = 0.22 (sec) , antiderivative size = 54, normalized size of antiderivative = 3.00 \[ \int (5-2 x)^6 (2+3 x)^3 (-16+33 x) \, dx=5184 \, x^{11} - 76896 \, x^{10} + 452304 \, x^{9} - 1256376 \, x^{8} + 1235404 \, x^{7} + 1497230 \, x^{6} - 3816225 \, x^{5} - \frac {98125}{2} \, x^{4} + 3987500 \, x^{3} - 37500 \, x^{2} - 2000000 \, x \]

[In]

integrate((5-2*x)^6*(2+3*x)^3*(-16+33*x),x, algorithm="fricas")

[Out]

5184*x^11 - 76896*x^10 + 452304*x^9 - 1256376*x^8 + 1235404*x^7 + 1497230*x^6 - 3816225*x^5 - 98125/2*x^4 + 39
87500*x^3 - 37500*x^2 - 2000000*x

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (15) = 30\).

Time = 0.03 (sec) , antiderivative size = 54, normalized size of antiderivative = 3.00 \[ \int (5-2 x)^6 (2+3 x)^3 (-16+33 x) \, dx=5184 x^{11} - 76896 x^{10} + 452304 x^{9} - 1256376 x^{8} + 1235404 x^{7} + 1497230 x^{6} - 3816225 x^{5} - \frac {98125 x^{4}}{2} + 3987500 x^{3} - 37500 x^{2} - 2000000 x \]

[In]

integrate((5-2*x)**6*(2+3*x)**3*(-16+33*x),x)

[Out]

5184*x**11 - 76896*x**10 + 452304*x**9 - 1256376*x**8 + 1235404*x**7 + 1497230*x**6 - 3816225*x**5 - 98125*x**
4/2 + 3987500*x**3 - 37500*x**2 - 2000000*x

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (16) = 32\).

Time = 0.19 (sec) , antiderivative size = 54, normalized size of antiderivative = 3.00 \[ \int (5-2 x)^6 (2+3 x)^3 (-16+33 x) \, dx=5184 \, x^{11} - 76896 \, x^{10} + 452304 \, x^{9} - 1256376 \, x^{8} + 1235404 \, x^{7} + 1497230 \, x^{6} - 3816225 \, x^{5} - \frac {98125}{2} \, x^{4} + 3987500 \, x^{3} - 37500 \, x^{2} - 2000000 \, x \]

[In]

integrate((5-2*x)^6*(2+3*x)^3*(-16+33*x),x, algorithm="maxima")

[Out]

5184*x^11 - 76896*x^10 + 452304*x^9 - 1256376*x^8 + 1235404*x^7 + 1497230*x^6 - 3816225*x^5 - 98125/2*x^4 + 39
87500*x^3 - 37500*x^2 - 2000000*x

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (16) = 32\).

Time = 0.28 (sec) , antiderivative size = 54, normalized size of antiderivative = 3.00 \[ \int (5-2 x)^6 (2+3 x)^3 (-16+33 x) \, dx=5184 \, x^{11} - 76896 \, x^{10} + 452304 \, x^{9} - 1256376 \, x^{8} + 1235404 \, x^{7} + 1497230 \, x^{6} - 3816225 \, x^{5} - \frac {98125}{2} \, x^{4} + 3987500 \, x^{3} - 37500 \, x^{2} - 2000000 \, x \]

[In]

integrate((5-2*x)^6*(2+3*x)^3*(-16+33*x),x, algorithm="giac")

[Out]

5184*x^11 - 76896*x^10 + 452304*x^9 - 1256376*x^8 + 1235404*x^7 + 1497230*x^6 - 3816225*x^5 - 98125/2*x^4 + 39
87500*x^3 - 37500*x^2 - 2000000*x

Mupad [B] (verification not implemented)

Time = 0.06 (sec) , antiderivative size = 54, normalized size of antiderivative = 3.00 \[ \int (5-2 x)^6 (2+3 x)^3 (-16+33 x) \, dx=5184\,x^{11}-76896\,x^{10}+452304\,x^9-1256376\,x^8+1235404\,x^7+1497230\,x^6-3816225\,x^5-\frac {98125\,x^4}{2}+3987500\,x^3-37500\,x^2-2000000\,x \]

[In]

int((3*x + 2)^3*(2*x - 5)^6*(33*x - 16),x)

[Out]

3987500*x^3 - 37500*x^2 - 2000000*x - (98125*x^4)/2 - 3816225*x^5 + 1497230*x^6 + 1235404*x^7 - 1256376*x^8 +
452304*x^9 - 76896*x^10 + 5184*x^11