\(\int (2+x^3)^2 \, dx\) [465]

Optimal result

Integrand size = 7, antiderivative size = 14 \[ \int \left (2+x^3\right )^2 \, dx=4 x+x^4+\frac {x^7}{7} \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {200} \[ \int \left (2+x^3\right )^2 \, dx=\frac {x^7}{7}+x^4+4 x \]

[In]

Int[(2 + x^3)^2,x]

[Out]

4*x + x^4 + x^7/7

Rule 200

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

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \left (2+x^3\right )^2 \, dx=4 x+x^4+\frac {x^7}{7} \]

[In]

Integrate[(2 + x^3)^2,x]

[Out]

4*x + x^4 + x^7/7

Maple [A] (verified)

Time = 0.79 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93

method	result	size
gosper	\(4 x +x^{4}+\frac {1}{7} x^{7}\)	\(13\)
default	\(4 x +x^{4}+\frac {1}{7} x^{7}\)	\(13\)
norman	\(4 x +x^{4}+\frac {1}{7} x^{7}\)	\(13\)
risch	\(4 x +x^{4}+\frac {1}{7} x^{7}\)	\(13\)
parallelrisch	\(4 x +x^{4}+\frac {1}{7} x^{7}\)	\(13\)

[In]

int((x^3+2)^2,x,method=_RETURNVERBOSE)

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \left (2+x^3\right )^2 \, dx=\frac {1}{7} \, x^{7} + x^{4} + 4 \, x \]

[In]

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

[Out]

1/7*x^7 + x^4 + 4*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \left (2+x^3\right )^2 \, dx=\frac {x^{7}}{7} + x^{4} + 4 x \]

[In]

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

[Out]

x**7/7 + x**4 + 4*x

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \left (2+x^3\right )^2 \, dx=\frac {1}{7} \, x^{7} + x^{4} + 4 \, x \]

[In]

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

[Out]

1/7*x^7 + x^4 + 4*x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \left (2+x^3\right )^2 \, dx=\frac {1}{7} \, x^{7} + x^{4} + 4 \, x \]

[In]

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

[Out]

1/7*x^7 + x^4 + 4*x

Mupad [B] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93 \[ \int \left (2+x^3\right )^2 \, dx=\frac {x\,\left (x^6+7\,x^3+28\right )}{7} \]

[In]

int((x^3 + 2)^2,x)

[Out]

(x*(7*x^3 + x^6 + 28))/7