3.49.94 \(\int (80 x+64 x^3) \, dx\)

Optimal. Leaf size=9 \[ \left (-5-4 x^2\right )^2 \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.22, number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 16 x^4+40 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[80*x + 64*x^3,x]

[Out]

40*x^2 + 16*x^4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=40 x^2+16 x^4\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 1.22 \begin {gather*} 40 x^2+16 x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[80*x + 64*x^3,x]

[Out]

40*x^2 + 16*x^4

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fricas [A]  time = 0.69, size = 11, normalized size = 1.22 \begin {gather*} 16 \, x^{4} + 40 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

16*x^4 + 40*x^2

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giac [A]  time = 0.13, size = 11, normalized size = 1.22 \begin {gather*} 16 \, x^{4} + 40 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

16*x^4 + 40*x^2

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maple [A]  time = 0.02, size = 12, normalized size = 1.33

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

16*x^4+40*x^2

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maxima [A]  time = 0.36, size = 11, normalized size = 1.22 \begin {gather*} 16 \, x^{4} + 40 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

16*x^4 + 40*x^2

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mupad [B]  time = 0.02, size = 12, normalized size = 1.33 \begin {gather*} 8\,x^2\,\left (2\,x^2+5\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(80*x + 64*x^3,x)

[Out]

8*x^2*(2*x^2 + 5)

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sympy [A]  time = 0.05, size = 8, normalized size = 0.89 \begin {gather*} 16 x^{4} + 40 x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

16*x**4 + 40*x**2

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