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*(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

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Rubi [A]  time = 0.0225944, antiderivative size = 56, normalized size of antiderivative = 1., 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*}

Mathematica [A]  time = 0.0019102, 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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Maple [A]  time = 0.001, size = 45, normalized size = 0.8 \begin{align*} 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 \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^2*(2+3*x)^4*(3+5*x)^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 = 1.03484, size = 59, normalized size = 1.05 \begin{align*} 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 \end{align*}

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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Fricas [A]  time = 1.31116, size = 135, normalized size = 2.41 \begin{align*} 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 \end{align*}

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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Sympy [A]  time = 0.065738, size = 49, normalized size = 0.88 \begin{align*} 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 \end{align*}

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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Giac [A]  time = 1.96286, size = 59, normalized size = 1.05 \begin{align*} 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 \end{align*}

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