\(\int (80 x+64 x^3) \, dx\) [4894]

Optimal result

Integrand size = 9, antiderivative size = 9 \[ \int \left (80 x+64 x^3\right ) \, dx=\left (-5-4 x^2\right )^2 \]

[Out]

(-4*x^2-5)^2

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.22, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (80 x+64 x^3\right ) \, dx=16 x^4+40 x^2 \]

[In]

Int[80*x + 64*x^3,x]

[Out]

40*x^2 + 16*x^4

Rubi steps \begin{align*} \text {integral}& = 40 x^2+16 x^4 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.22 \[ \int \left (80 x+64 x^3\right ) \, dx=40 x^2+16 x^4 \]

[In]

Integrate[80*x + 64*x^3,x]

[Out]

40*x^2 + 16*x^4

Maple [A] (verified)

Time = 0.05 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.11

method	result	size
default	\(\left (4 x^{2}+5\right )^{2}\)	\(10\)
norman	\(16 x^{4}+40 x^{2}\)	\(12\)
risch	\(16 x^{4}+40 x^{2}\)	\(12\)
parallelrisch	\(16 x^{4}+40 x^{2}\)	\(12\)
parts	\(16 x^{4}+40 x^{2}\)	\(12\)
gosper	\(8 x^{2} \left (2 x^{2}+5\right )\)	\(13\)

[In]

int(64*x^3+80*x,x,method=_RETURNVERBOSE)

[Out]

(4*x^2+5)^2

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.22 \[ \int \left (80 x+64 x^3\right ) \, dx=16 \, x^{4} + 40 \, x^{2} \]

[In]

integrate(64*x^3+80*x,x, algorithm="fricas")

[Out]

16*x^4 + 40*x^2

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.89 \[ \int \left (80 x+64 x^3\right ) \, dx=16 x^{4} + 40 x^{2} \]

[In]

integrate(64*x**3+80*x,x)

[Out]

16*x**4 + 40*x**2

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.22 \[ \int \left (80 x+64 x^3\right ) \, dx=16 \, x^{4} + 40 \, x^{2} \]

[In]

integrate(64*x^3+80*x,x, algorithm="maxima")

[Out]

16*x^4 + 40*x^2

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.22 \[ \int \left (80 x+64 x^3\right ) \, dx=16 \, x^{4} + 40 \, x^{2} \]

[In]

integrate(64*x^3+80*x,x, algorithm="giac")

[Out]

16*x^4 + 40*x^2

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.33 \[ \int \left (80 x+64 x^3\right ) \, dx=8\,x^2\,\left (2\,x^2+5\right ) \]

[In]

int(80*x + 64*x^3,x)

[Out]

8*x^2*(2*x^2 + 5)