\(\int (8+8 x-x^3+8 x^4) \, dx\) [48]

Optimal result

Integrand size = 15, antiderivative size = 23 \[ \int \left (8+8 x-x^3+8 x^4\right ) \, dx=8 x+4 x^2-\frac {x^4}{4}+\frac {8 x^5}{5} \]

[Out]

8*x+4*x^2-1/4*x^4+8/5*x^5

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (8+8 x-x^3+8 x^4\right ) \, dx=\frac {8 x^5}{5}-\frac {x^4}{4}+4 x^2+8 x \]

[In]

Int[8 + 8*x - x^3 + 8*x^4,x]

[Out]

8*x + 4*x^2 - x^4/4 + (8*x^5)/5

Rubi steps \begin{align*} \text {integral}& = 8 x+4 x^2-\frac {x^4}{4}+\frac {8 x^5}{5} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00 \[ \int \left (8+8 x-x^3+8 x^4\right ) \, dx=8 x+4 x^2-\frac {x^4}{4}+\frac {8 x^5}{5} \]

[In]

Integrate[8 + 8*x - x^3 + 8*x^4,x]

[Out]

8*x + 4*x^2 - x^4/4 + (8*x^5)/5

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87

method	result	size
gosper	\(8 x +4 x^{2}-\frac {1}{4} x^{4}+\frac {8}{5} x^{5}\)	\(20\)
default	\(8 x +4 x^{2}-\frac {1}{4} x^{4}+\frac {8}{5} x^{5}\)	\(20\)
norman	\(8 x +4 x^{2}-\frac {1}{4} x^{4}+\frac {8}{5} x^{5}\)	\(20\)
risch	\(8 x +4 x^{2}-\frac {1}{4} x^{4}+\frac {8}{5} x^{5}\)	\(20\)
parallelrisch	\(8 x +4 x^{2}-\frac {1}{4} x^{4}+\frac {8}{5} x^{5}\)	\(20\)
parts	\(8 x +4 x^{2}-\frac {1}{4} x^{4}+\frac {8}{5} x^{5}\)	\(20\)

[In]

int(8*x^4-x^3+8*x+8,x,method=_RETURNVERBOSE)

[Out]

8*x+4*x^2-1/4*x^4+8/5*x^5

Fricas [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \left (8+8 x-x^3+8 x^4\right ) \, dx=\frac {8}{5} \, x^{5} - \frac {1}{4} \, x^{4} + 4 \, x^{2} + 8 \, x \]

[In]

integrate(8*x^4-x^3+8*x+8,x, algorithm="fricas")

[Out]

8/5*x^5 - 1/4*x^4 + 4*x^2 + 8*x

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \left (8+8 x-x^3+8 x^4\right ) \, dx=\frac {8 x^{5}}{5} - \frac {x^{4}}{4} + 4 x^{2} + 8 x \]

[In]

integrate(8*x**4-x**3+8*x+8,x)

[Out]

8*x**5/5 - x**4/4 + 4*x**2 + 8*x

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \left (8+8 x-x^3+8 x^4\right ) \, dx=\frac {8}{5} \, x^{5} - \frac {1}{4} \, x^{4} + 4 \, x^{2} + 8 \, x \]

[In]

integrate(8*x^4-x^3+8*x+8,x, algorithm="maxima")

[Out]

8/5*x^5 - 1/4*x^4 + 4*x^2 + 8*x

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \left (8+8 x-x^3+8 x^4\right ) \, dx=\frac {8}{5} \, x^{5} - \frac {1}{4} \, x^{4} + 4 \, x^{2} + 8 \, x \]

[In]

integrate(8*x^4-x^3+8*x+8,x, algorithm="giac")

[Out]

8/5*x^5 - 1/4*x^4 + 4*x^2 + 8*x

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \left (8+8 x-x^3+8 x^4\right ) \, dx=\frac {8\,x^5}{5}-\frac {x^4}{4}+4\,x^2+8\,x \]

[In]

int(8*x - x^3 + 8*x^4 + 8,x)

[Out]

8*x + 4*x^2 - x^4/4 + (8*x^5)/5