3.73 \(\int (3-19 x^2+32 x^4-16 x^6) \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.0031791, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ -\frac{16 x^7}{7}+\frac{32 x^5}{5}-\frac{19 x^3}{3}+3 x \]

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*}

Mathematica [A]  time = 0.0000443, size = 25, normalized size = 1. \[ -\frac{16 x^7}{7}+\frac{32 x^5}{5}-\frac{19 x^3}{3}+3 x \]

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., size = 20, normalized size = 0.8 \begin{align*} 3\,x-{\frac{19\,{x}^{3}}{3}}+{\frac{32\,{x}^{5}}{5}}-{\frac{16\,{x}^{7}}{7}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 1.17189, size = 26, normalized size = 1.04 \begin{align*} -\frac{16}{7} \, x^{7} + \frac{32}{5} \, x^{5} - \frac{19}{3} \, x^{3} + 3 \, x \end{align*}

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 = 1.43674, size = 53, normalized size = 2.12 \begin{align*} -\frac{16}{7} x^{7} + \frac{32}{5} x^{5} - \frac{19}{3} x^{3} + 3 x \end{align*}

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 = 0.05443, size = 22, normalized size = 0.88 \begin{align*} - \frac{16 x^{7}}{7} + \frac{32 x^{5}}{5} - \frac{19 x^{3}}{3} + 3 x \end{align*}

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 = 1.12437, size = 26, normalized size = 1.04 \begin{align*} -\frac{16}{7} \, x^{7} + \frac{32}{5} \, x^{5} - \frac{19}{3} \, x^{3} + 3 \, x \end{align*}

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