3.1257 \(\int (1-2 x)^2 (2+3 x)^4 (3+5 x)^2 \, dx\)

Optimal. Leaf size=56 \[ \frac {100 (3 x+2)^9}{2187}-\frac {185}{486} (3 x+2)^8+\frac {503}{567} (3 x+2)^7-\frac {259}{729} (3 x+2)^6+\frac {49 (3 x+2)^5}{1215} \]

[Out]

49/1215*(2+3*x)^5-259/729*(2+3*x)^6+503/567*(2+3*x)^7-185/486*(2+3*x)^8+100/2187*(2+3*x)^9

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Rubi [A]  time = 0.02, antiderivative size = 56, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \[ \frac {100 (3 x+2)^9}{2187}-\frac {185}{486} (3 x+2)^8+\frac {503}{567} (3 x+2)^7-\frac {259}{729} (3 x+2)^6+\frac {49 (3 x+2)^5}{1215} \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^2,x]

[Out]

(49*(2 + 3*x)^5)/1215 - (259*(2 + 3*x)^6)/729 + (503*(2 + 3*x)^7)/567 - (185*(2 + 3*x)^8)/486 + (100*(2 + 3*x)
^9)/2187

Rule 88

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*} \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^2 \, dx &=\int \left (\frac {49}{81} (2+3 x)^4-\frac {518}{81} (2+3 x)^5+\frac {503}{27} (2+3 x)^6-\frac {740}{81} (2+3 x)^7+\frac {100}{81} (2+3 x)^8\right ) \, dx\\ &=\frac {49 (2+3 x)^5}{1215}-\frac {259}{729} (2+3 x)^6+\frac {503}{567} (2+3 x)^7-\frac {185}{486} (2+3 x)^8+\frac {100 (2+3 x)^9}{2187}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 52, normalized size = 0.93 \[ 900 x^9+\frac {5805 x^8}{2}+\frac {21141 x^7}{7}+115 x^6-\frac {9791 x^5}{5}-1174 x^4+\frac {424 x^3}{3}+384 x^2+144 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^2,x]

[Out]

144*x + 384*x^2 + (424*x^3)/3 - 1174*x^4 - (9791*x^5)/5 + 115*x^6 + (21141*x^7)/7 + (5805*x^8)/2 + 900*x^9

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fricas [A]  time = 0.42, size = 44, normalized size = 0.79 \[ 900 x^{9} + \frac {5805}{2} x^{8} + \frac {21141}{7} x^{7} + 115 x^{6} - \frac {9791}{5} x^{5} - 1174 x^{4} + \frac {424}{3} x^{3} + 384 x^{2} + 144 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^4*(3+5*x)^2,x, algorithm="fricas")

[Out]

900*x^9 + 5805/2*x^8 + 21141/7*x^7 + 115*x^6 - 9791/5*x^5 - 1174*x^4 + 424/3*x^3 + 384*x^2 + 144*x

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giac [A]  time = 1.21, size = 44, normalized size = 0.79 \[ 900 \, x^{9} + \frac {5805}{2} \, x^{8} + \frac {21141}{7} \, x^{7} + 115 \, x^{6} - \frac {9791}{5} \, x^{5} - 1174 \, x^{4} + \frac {424}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^4*(3+5*x)^2,x, algorithm="giac")

[Out]

900*x^9 + 5805/2*x^8 + 21141/7*x^7 + 115*x^6 - 9791/5*x^5 - 1174*x^4 + 424/3*x^3 + 384*x^2 + 144*x

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maple [A]  time = 0.00, size = 45, normalized size = 0.80 \[ 900 x^{9}+\frac {5805}{2} x^{8}+\frac {21141}{7} x^{7}+115 x^{6}-\frac {9791}{5} x^{5}-1174 x^{4}+\frac {424}{3} x^{3}+384 x^{2}+144 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^2*(3*x+2)^4*(5*x+3)^2,x)

[Out]

900*x^9+5805/2*x^8+21141/7*x^7+115*x^6-9791/5*x^5-1174*x^4+424/3*x^3+384*x^2+144*x

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maxima [A]  time = 0.72, size = 44, normalized size = 0.79 \[ 900 \, x^{9} + \frac {5805}{2} \, x^{8} + \frac {21141}{7} \, x^{7} + 115 \, x^{6} - \frac {9791}{5} \, x^{5} - 1174 \, x^{4} + \frac {424}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^4*(3+5*x)^2,x, algorithm="maxima")

[Out]

900*x^9 + 5805/2*x^8 + 21141/7*x^7 + 115*x^6 - 9791/5*x^5 - 1174*x^4 + 424/3*x^3 + 384*x^2 + 144*x

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mupad [B]  time = 0.04, size = 44, normalized size = 0.79 \[ 900\,x^9+\frac {5805\,x^8}{2}+\frac {21141\,x^7}{7}+115\,x^6-\frac {9791\,x^5}{5}-1174\,x^4+\frac {424\,x^3}{3}+384\,x^2+144\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x - 1)^2*(3*x + 2)^4*(5*x + 3)^2,x)

[Out]

144*x + 384*x^2 + (424*x^3)/3 - 1174*x^4 - (9791*x^5)/5 + 115*x^6 + (21141*x^7)/7 + (5805*x^8)/2 + 900*x^9

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sympy [A]  time = 0.07, size = 49, normalized size = 0.88 \[ 900 x^{9} + \frac {5805 x^{8}}{2} + \frac {21141 x^{7}}{7} + 115 x^{6} - \frac {9791 x^{5}}{5} - 1174 x^{4} + \frac {424 x^{3}}{3} + 384 x^{2} + 144 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**2*(2+3*x)**4*(3+5*x)**2,x)

[Out]

900*x**9 + 5805*x**8/2 + 21141*x**7/7 + 115*x**6 - 9791*x**5/5 - 1174*x**4 + 424*x**3/3 + 384*x**2 + 144*x

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