3.52.41 \(\int (-2+3 x^2) \, dx\)

Optimal. Leaf size=17 \[ 2 \left (\frac {13}{2}+e-x+\frac {x^3}{2}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.41, number of steps used = 1, number of rules used = 0, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x^3-2 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-2 + 3*x^2,x]

[Out]

-2*x + x^3

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-2 x+x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 0.41 \begin {gather*} -2 x+x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-2 + 3*x^2,x]

[Out]

-2*x + x^3

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fricas [A]  time = 0.56, size = 7, normalized size = 0.41 \begin {gather*} x^{3} - 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x^2-2,x, algorithm="fricas")

[Out]

x^3 - 2*x

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giac [A]  time = 0.16, size = 7, normalized size = 0.41 \begin {gather*} x^{3} - 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x^2-2,x, algorithm="giac")

[Out]

x^3 - 2*x

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maple [A]  time = 0.01, size = 8, normalized size = 0.47

method	result	size
gosper	\(x^{3}-2 x\)	\(8\)
default	\(x^{3}-2 x\)	\(8\)
norman	\(x^{3}-2 x\)	\(8\)
risch	\(x^{3}-2 x\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*x^2-2,x,method=_RETURNVERBOSE)

[Out]

x^3-2*x

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maxima [A]  time = 0.39, size = 7, normalized size = 0.41 \begin {gather*} x^{3} - 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x^2-2,x, algorithm="maxima")

[Out]

x^3 - 2*x

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mupad [B]  time = 0.01, size = 7, normalized size = 0.41 \begin {gather*} x^3-2\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*x^2 - 2,x)

[Out]

x^3 - 2*x

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sympy [A]  time = 0.04, size = 5, normalized size = 0.29 \begin {gather*} x^{3} - 2 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x**2-2,x)

[Out]

x**3 - 2*x

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