3.370 \(\int x^2 (1+x^3)^4 \, dx\)

Optimal. Leaf size=11 \[ \frac {1}{15} \left (x^3+1\right )^5 \]

[Out]

1/15*(x^3+1)^5

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {261} \[ \frac {1}{15} \left (x^3+1\right )^5 \]

Antiderivative was successfully verified.

[In]

Int[x^2*(1 + x^3)^4,x]

[Out]

(1 + x^3)^5/15

Rule 261

Int[(x_)^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[(a + b*x^n)^(p + 1)/(b*n*(p + 1)), x] /; FreeQ
[{a, b, m, n, p}, x] && EqQ[m, n - 1] && NeQ[p, -1]

Rubi steps

\begin {align*} \int x^2 \left (1+x^3\right )^4 \, dx &=\frac {1}{15} \left (1+x^3\right )^5\\ \end {align*}

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Mathematica [B]  time = 0.00, size = 36, normalized size = 3.27 \[ \frac {x^{15}}{15}+\frac {x^{12}}{3}+\frac {2 x^9}{3}+\frac {2 x^6}{3}+\frac {x^3}{3} \]

Antiderivative was successfully verified.

[In]

Integrate[x^2*(1 + x^3)^4,x]

[Out]

x^3/3 + (2*x^6)/3 + (2*x^9)/3 + x^12/3 + x^15/15

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fricas [B]  time = 0.34, size = 26, normalized size = 2.36 \[ \frac {1}{15} x^{15} + \frac {1}{3} x^{12} + \frac {2}{3} x^{9} + \frac {2}{3} x^{6} + \frac {1}{3} x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/15*x^15 + 1/3*x^12 + 2/3*x^9 + 2/3*x^6 + 1/3*x^3

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giac [A]  time = 0.87, size = 9, normalized size = 0.82 \[ \frac {1}{15} \, {\left (x^{3} + 1\right )}^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/15*(x^3 + 1)^5

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maple [B]  time = 0.00, size = 27, normalized size = 2.45 \[ \frac {1}{15} x^{15}+\frac {1}{3} x^{12}+\frac {2}{3} x^{9}+\frac {2}{3} x^{6}+\frac {1}{3} x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/15*x^15+1/3*x^12+2/3*x^9+2/3*x^6+1/3*x^3

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maxima [A]  time = 0.42, size = 9, normalized size = 0.82 \[ \frac {1}{15} \, {\left (x^{3} + 1\right )}^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/15*(x^3 + 1)^5

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mupad [B]  time = 0.02, size = 26, normalized size = 2.36 \[ \frac {x^{15}}{15}+\frac {x^{12}}{3}+\frac {2\,x^9}{3}+\frac {2\,x^6}{3}+\frac {x^3}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^2*(x^3 + 1)^4,x)

[Out]

x^3/3 + (2*x^6)/3 + (2*x^9)/3 + x^12/3 + x^15/15

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sympy [B]  time = 0.06, size = 27, normalized size = 2.45 \[ \frac {x^{15}}{15} + \frac {x^{12}}{3} + \frac {2 x^{9}}{3} + \frac {2 x^{6}}{3} + \frac {x^{3}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x**15/15 + x**12/3 + 2*x**9/3 + 2*x**6/3 + x**3/3

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