3.465 \(\int (2+x^3)^2 \, dx\)

Optimal. Leaf size=14 \[ \frac{x^7}{7}+x^4+4 x \]

[Out]

4*x + x^4 + x^7/7

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Rubi [A]  time = 0.0036466, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {194} \[ \frac{x^7}{7}+x^4+4 x \]

Antiderivative was successfully verified.

[In]

Int[(2 + x^3)^2,x]

[Out]

4*x + x^4 + x^7/7

Rule 194

Int[((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Int[ExpandIntegrand[(a + b*x^n)^p, x], x] /; FreeQ[{a, b}, x]
&& IGtQ[n, 0] && IGtQ[p, 0]

Rubi steps

\begin{align*} \int \left (2+x^3\right )^2 \, dx &=\int \left (4+4 x^3+x^6\right ) \, dx\\ &=4 x+x^4+\frac{x^7}{7}\\ \end{align*}

Mathematica [A]  time = 0.0004188, size = 14, normalized size = 1. \[ \frac{x^7}{7}+x^4+4 x \]

Antiderivative was successfully verified.

[In]

Integrate[(2 + x^3)^2,x]

[Out]

4*x + x^4 + x^7/7

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Maple [A]  time = 0.001, size = 13, normalized size = 0.9 \begin{align*} 4\,x+{x}^{4}+{\frac{{x}^{7}}{7}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x^3+2)^2,x)

[Out]

4*x+x^4+1/7*x^7

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Maxima [A]  time = 1.04816, size = 16, normalized size = 1.14 \begin{align*} \frac{1}{7} \, x^{7} + x^{4} + 4 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/7*x^7 + x^4 + 4*x

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Fricas [A]  time = 1.0112, size = 28, normalized size = 2. \begin{align*} \frac{1}{7} x^{7} + x^{4} + 4 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/7*x^7 + x^4 + 4*x

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Sympy [A]  time = 0.049103, size = 10, normalized size = 0.71 \begin{align*} \frac{x^{7}}{7} + x^{4} + 4 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x**7/7 + x**4 + 4*x

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Giac [A]  time = 1.12614, size = 16, normalized size = 1.14 \begin{align*} \frac{1}{7} \, x^{7} + x^{4} + 4 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/7*x^7 + x^4 + 4*x