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-19/3*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 = {} \[ -\frac {16 x^7}{7}+\frac {32 x^5}{5}-\frac {19 x^3}{3}+3 x \]

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*}

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

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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fricas [A]  time = 0.72, size = 19, normalized size = 0.76 \[ -\frac {16}{7} x^{7} + \frac {32}{5} x^{5} - \frac {19}{3} x^{3} + 3 x \]

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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giac [A]  time = 0.28, size = 19, normalized size = 0.76 \[ -\frac {16}{7} \, x^{7} + \frac {32}{5} \, x^{5} - \frac {19}{3} \, x^{3} + 3 \, x \]

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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maple [A]  time = 0.00, size = 20, normalized size = 0.80 \[ -\frac {16}{7} x^{7}+\frac {32}{5} x^{5}-\frac {19}{3} x^{3}+3 x \]

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 = 0.64, size = 19, normalized size = 0.76 \[ -\frac {16}{7} \, x^{7} + \frac {32}{5} \, x^{5} - \frac {19}{3} \, x^{3} + 3 \, x \]

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

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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sympy [A]  time = 0.06, size = 22, normalized size = 0.88 \[ - \frac {16 x^{7}}{7} + \frac {32 x^{5}}{5} - \frac {19 x^{3}}{3} + 3 x \]

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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