3.1.73 \(\int (3-19 x^2+32 x^4-16 x^6) \, dx\) [73]

Optimal. Leaf size=25 \[ 3 x-\frac {19 x^3}{3}+\frac {32 x^5}{5}-\frac {16 x^7}{7} \]

[Out]

3*x-19/3*x^3+32/5*x^5-16/7*x^7

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Rubi [A]
time = 0.00, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -\frac {16 x^7}{7}+\frac {32 x^5}{5}-\frac {19 x^3}{3}+3 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[3 - 19*x^2 + 32*x^4 - 16*x^6,x]

[Out]

3*x - (19*x^3)/3 + (32*x^5)/5 - (16*x^7)/7

Rubi steps

\begin {align*} \int \left (3-19 x^2+32 x^4-16 x^6\right ) \, dx &=3 x-\frac {19 x^3}{3}+\frac {32 x^5}{5}-\frac {16 x^7}{7}\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 25, normalized size = 1.00 \begin {gather*} 3 x-\frac {19 x^3}{3}+\frac {32 x^5}{5}-\frac {16 x^7}{7} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3 - 19*x^2 + 32*x^4 - 16*x^6,x]

[Out]

3*x - (19*x^3)/3 + (32*x^5)/5 - (16*x^7)/7

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Maple [A]
time = 0.03, size = 20, normalized size = 0.80

method	result	size
default	\(3 x -\frac {19}{3} x^{3}+\frac {32}{5} x^{5}-\frac {16}{7} x^{7}\)	\(20\)
norman	\(3 x -\frac {19}{3} x^{3}+\frac {32}{5} x^{5}-\frac {16}{7} x^{7}\)	\(20\)
risch	\(3 x -\frac {19}{3} x^{3}+\frac {32}{5} x^{5}-\frac {16}{7} x^{7}\)	\(20\)
gosper	\(-\frac {x \left (240 x^{6}-672 x^{4}+665 x^{2}-315\right )}{105}\)	\(21\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-16*x^6+32*x^4-19*x^2+3,x,method=_RETURNVERBOSE)

[Out]

3*x-19/3*x^3+32/5*x^5-16/7*x^7

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Maxima [A]
time = 0.27, size = 19, normalized size = 0.76 \begin {gather*} -\frac {16}{7} \, x^{7} + \frac {32}{5} \, x^{5} - \frac {19}{3} \, x^{3} + 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-16*x^6+32*x^4-19*x^2+3,x, algorithm="maxima")

[Out]

-16/7*x^7 + 32/5*x^5 - 19/3*x^3 + 3*x

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Fricas [A]
time = 0.36, size = 19, normalized size = 0.76 \begin {gather*} -\frac {16}{7} \, x^{7} + \frac {32}{5} \, x^{5} - \frac {19}{3} \, x^{3} + 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-16*x^6+32*x^4-19*x^2+3,x, algorithm="fricas")

[Out]

-16/7*x^7 + 32/5*x^5 - 19/3*x^3 + 3*x

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Sympy [A]
time = 0.01, size = 22, normalized size = 0.88 \begin {gather*} - \frac {16 x^{7}}{7} + \frac {32 x^{5}}{5} - \frac {19 x^{3}}{3} + 3 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-16*x**6+32*x**4-19*x**2+3,x)

[Out]

-16*x**7/7 + 32*x**5/5 - 19*x**3/3 + 3*x

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Giac [A]
time = 4.05, size = 19, normalized size = 0.76 \begin {gather*} -\frac {16}{7} \, x^{7} + \frac {32}{5} \, x^{5} - \frac {19}{3} \, x^{3} + 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-16*x^6+32*x^4-19*x^2+3,x, algorithm="giac")

[Out]

-16/7*x^7 + 32/5*x^5 - 19/3*x^3 + 3*x

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Mupad [B]
time = 0.03, size = 19, normalized size = 0.76 \begin {gather*} -\frac {16\,x^7}{7}+\frac {32\,x^5}{5}-\frac {19\,x^3}{3}+3\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(32*x^4 - 19*x^2 - 16*x^6 + 3,x)

[Out]

3*x - (19*x^3)/3 + (32*x^5)/5 - (16*x^7)/7

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