3.16 \(\int (3-x+2 x^2) (2+3 x+5 x^2)^3 \, dx\)

Optimal. Leaf size=56 \[ \frac{250 x^9}{9}+\frac{325 x^8}{8}+\frac{720 x^7}{7}+134 x^6+\frac{876 x^5}{5}+\frac{579 x^4}{4}+\frac{322 x^3}{3}+50 x^2+24 x \]

[Out]

24*x + 50*x^2 + (322*x^3)/3 + (579*x^4)/4 + (876*x^5)/5 + 134*x^6 + (720*x^7)/7 + (325*x^8)/8 + (250*x^9)/9

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Rubi [A]  time = 0.0377753, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.043, Rules used = {1657} \[ \frac{250 x^9}{9}+\frac{325 x^8}{8}+\frac{720 x^7}{7}+134 x^6+\frac{876 x^5}{5}+\frac{579 x^4}{4}+\frac{322 x^3}{3}+50 x^2+24 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

24*x + 50*x^2 + (322*x^3)/3 + (579*x^4)/4 + (876*x^5)/5 + 134*x^6 + (720*x^7)/7 + (325*x^8)/8 + (250*x^9)/9

Rule 1657

Int[(Pq_)*((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[ExpandIntegrand[Pq*(a + b*x + c*x^2)^p, x
], x] /; FreeQ[{a, b, c}, x] && PolyQ[Pq, x] && IGtQ[p, -2]

Rubi steps

\begin{align*} \int \left (3-x+2 x^2\right ) \left (2+3 x+5 x^2\right )^3 \, dx &=\int \left (24+100 x+322 x^2+579 x^3+876 x^4+804 x^5+720 x^6+325 x^7+250 x^8\right ) \, dx\\ &=24 x+50 x^2+\frac{322 x^3}{3}+\frac{579 x^4}{4}+\frac{876 x^5}{5}+134 x^6+\frac{720 x^7}{7}+\frac{325 x^8}{8}+\frac{250 x^9}{9}\\ \end{align*}

Mathematica [A]  time = 0.0017287, size = 56, normalized size = 1. \[ \frac{250 x^9}{9}+\frac{325 x^8}{8}+\frac{720 x^7}{7}+134 x^6+\frac{876 x^5}{5}+\frac{579 x^4}{4}+\frac{322 x^3}{3}+50 x^2+24 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

24*x + 50*x^2 + (322*x^3)/3 + (579*x^4)/4 + (876*x^5)/5 + 134*x^6 + (720*x^7)/7 + (325*x^8)/8 + (250*x^9)/9

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Maple [A]  time = 0.044, size = 45, normalized size = 0.8 \begin{align*} 24\,x+50\,{x}^{2}+{\frac{322\,{x}^{3}}{3}}+{\frac{579\,{x}^{4}}{4}}+{\frac{876\,{x}^{5}}{5}}+134\,{x}^{6}+{\frac{720\,{x}^{7}}{7}}+{\frac{325\,{x}^{8}}{8}}+{\frac{250\,{x}^{9}}{9}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

24*x+50*x^2+322/3*x^3+579/4*x^4+876/5*x^5+134*x^6+720/7*x^7+325/8*x^8+250/9*x^9

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Maxima [A]  time = 0.983348, size = 59, normalized size = 1.05 \begin{align*} \frac{250}{9} \, x^{9} + \frac{325}{8} \, x^{8} + \frac{720}{7} \, x^{7} + 134 \, x^{6} + \frac{876}{5} \, x^{5} + \frac{579}{4} \, x^{4} + \frac{322}{3} \, x^{3} + 50 \, x^{2} + 24 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

250/9*x^9 + 325/8*x^8 + 720/7*x^7 + 134*x^6 + 876/5*x^5 + 579/4*x^4 + 322/3*x^3 + 50*x^2 + 24*x

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Fricas [A]  time = 0.716507, size = 131, normalized size = 2.34 \begin{align*} \frac{250}{9} x^{9} + \frac{325}{8} x^{8} + \frac{720}{7} x^{7} + 134 x^{6} + \frac{876}{5} x^{5} + \frac{579}{4} x^{4} + \frac{322}{3} x^{3} + 50 x^{2} + 24 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

250/9*x^9 + 325/8*x^8 + 720/7*x^7 + 134*x^6 + 876/5*x^5 + 579/4*x^4 + 322/3*x^3 + 50*x^2 + 24*x

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Sympy [A]  time = 0.084274, size = 53, normalized size = 0.95 \begin{align*} \frac{250 x^{9}}{9} + \frac{325 x^{8}}{8} + \frac{720 x^{7}}{7} + 134 x^{6} + \frac{876 x^{5}}{5} + \frac{579 x^{4}}{4} + \frac{322 x^{3}}{3} + 50 x^{2} + 24 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

250*x**9/9 + 325*x**8/8 + 720*x**7/7 + 134*x**6 + 876*x**5/5 + 579*x**4/4 + 322*x**3/3 + 50*x**2 + 24*x

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Giac [A]  time = 1.17455, size = 59, normalized size = 1.05 \begin{align*} \frac{250}{9} \, x^{9} + \frac{325}{8} \, x^{8} + \frac{720}{7} \, x^{7} + 134 \, x^{6} + \frac{876}{5} \, x^{5} + \frac{579}{4} \, x^{4} + \frac{322}{3} \, x^{3} + 50 \, x^{2} + 24 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

250/9*x^9 + 325/8*x^8 + 720/7*x^7 + 134*x^6 + 876/5*x^5 + 579/4*x^4 + 322/3*x^3 + 50*x^2 + 24*x