3.87.57 \(\int (-1-60 x+900 x^3) \, dx\)

Optimal. Leaf size=16 \[ -3-x+\left (-1+15 x^2\right )^2+\log (9) \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 0.88, number of steps used = 1, number of rules used = 0, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 225 x^4-30 x^2-x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 - 60*x + 900*x^3,x]

[Out]

-x - 30*x^2 + 225*x^4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-x-30 x^2+225 x^4\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 0.88 \begin {gather*} -x-30 x^2+225 x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 - 60*x + 900*x^3,x]

[Out]

-x - 30*x^2 + 225*x^4

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fricas [A]  time = 0.54, size = 14, normalized size = 0.88 \begin {gather*} 225 \, x^{4} - 30 \, x^{2} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(900*x^3-60*x-1,x, algorithm="fricas")

[Out]

225*x^4 - 30*x^2 - x

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giac [A]  time = 0.20, size = 14, normalized size = 0.88 \begin {gather*} 225 \, x^{4} - 30 \, x^{2} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(900*x^3-60*x-1,x, algorithm="giac")

[Out]

225*x^4 - 30*x^2 - x

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maple [A]  time = 0.02, size = 15, normalized size = 0.94

method	result	size
gosper	\(225 x^{4}-30 x^{2}-x\)	\(15\)
default	\(225 x^{4}-30 x^{2}-x\)	\(15\)
norman	\(225 x^{4}-30 x^{2}-x\)	\(15\)
risch	\(225 x^{4}-30 x^{2}-x\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(900*x^3-60*x-1,x,method=_RETURNVERBOSE)

[Out]

225*x^4-30*x^2-x

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maxima [A]  time = 0.36, size = 14, normalized size = 0.88 \begin {gather*} 225 \, x^{4} - 30 \, x^{2} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(900*x^3-60*x-1,x, algorithm="maxima")

[Out]

225*x^4 - 30*x^2 - x

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mupad [B]  time = 0.03, size = 13, normalized size = 0.81 \begin {gather*} -x\,\left (-225\,x^3+30\,x+1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(900*x^3 - 60*x - 1,x)

[Out]

-x*(30*x - 225*x^3 + 1)

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sympy [A]  time = 0.05, size = 10, normalized size = 0.62 \begin {gather*} 225 x^{4} - 30 x^{2} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(900*x**3-60*x-1,x)

[Out]

225*x**4 - 30*x**2 - x

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