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

Optimal. Leaf size=18 \[ -\frac {1}{2} (5-2 x)^7 (3 x+2)^4 \]

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Rubi [A]  time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {74} \begin {gather*} -\frac {1}{2} (5-2 x)^7 (3 x+2)^4 \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-((5 - 2*x)^7*(2 + 3*x)^4)/2

Rule 74

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*} \int (5-2 x)^6 (2+3 x)^3 (-16+33 x) \, dx &=-\frac {1}{2} (5-2 x)^7 (2+3 x)^4\\ \end {align*}

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Mathematica [B]  time = 0.00, size = 56, normalized size = 3.11 \begin {gather*} 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 \end {gather*}

Antiderivative was successfully verified.

[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

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (5-2 x)^6 (2+3 x)^3 (-16+33 x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [B]  time = 1.67, size = 54, normalized size = 3.00 \begin {gather*} 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 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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giac [B]  time = 1.20, size = 54, normalized size = 3.00 \begin {gather*} 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 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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maple [B]  time = 0.00, size = 55, normalized size = 3.06 \begin {gather*} 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 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((5-2*x)^6*(3*x+2)^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^5-98125/2*x^4+3987500*x^3-37500*
x^2-2000000*x

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maxima [B]  time = 0.51, size = 54, normalized size = 3.00 \begin {gather*} 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 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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mupad [B]  time = 0.06, size = 54, normalized size = 3.00 \begin {gather*} 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 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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sympy [B]  time = 0.08, size = 54, normalized size = 3.00 \begin {gather*} 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 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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