3.35.88 \(\int \frac {-2+144 x^2}{33-2 x+48 x^3} \, dx\)

Optimal. Leaf size=19 \[ \log \left (-2+\frac {1}{4} \left (-3+\frac {2 x}{3}-16 x^3\right )\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 11, normalized size of antiderivative = 0.58, number of steps used = 1, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {1587} \begin {gather*} \log \left (48 x^3-2 x+33\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-2 + 144*x^2)/(33 - 2*x + 48*x^3),x]

[Out]

Log[33 - 2*x + 48*x^3]

Rule 1587

Int[(Pp_)/(Qq_), x_Symbol] :> With[{p = Expon[Pp, x], q = Expon[Qq, x]}, Simp[(Coeff[Pp, x, p]*Log[RemoveConte
nt[Qq, x]])/(q*Coeff[Qq, x, q]), x] /; EqQ[p, q - 1] && EqQ[Pp, Simplify[(Coeff[Pp, x, p]*D[Qq, x])/(q*Coeff[Q
q, x, q])]]] /; PolyQ[Pp, x] && PolyQ[Qq, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\log \left (33-2 x+48 x^3\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 11, normalized size = 0.58 \begin {gather*} \log \left (33-2 x+48 x^3\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2 + 144*x^2)/(33 - 2*x + 48*x^3),x]

[Out]

Log[33 - 2*x + 48*x^3]

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fricas [A]  time = 0.60, size = 11, normalized size = 0.58 \begin {gather*} \log \left (48 \, x^{3} - 2 \, x + 33\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((144*x^2-2)/(48*x^3-2*x+33),x, algorithm="fricas")

[Out]

log(48*x^3 - 2*x + 33)

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giac [A]  time = 0.14, size = 12, normalized size = 0.63 \begin {gather*} \log \left ({\left | 48 \, x^{3} - 2 \, x + 33 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((144*x^2-2)/(48*x^3-2*x+33),x, algorithm="giac")

[Out]

log(abs(48*x^3 - 2*x + 33))

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maple [A]  time = 0.02, size = 12, normalized size = 0.63

method	result	size
derivativedivides	\(\ln \left (48 x^{3}-2 x +33\right )\)	\(12\)
default	\(\ln \left (48 x^{3}-2 x +33\right )\)	\(12\)
norman	\(\ln \left (48 x^{3}-2 x +33\right )\)	\(12\)
risch	\(\ln \left (48 x^{3}-2 x +33\right )\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((144*x^2-2)/(48*x^3-2*x+33),x,method=_RETURNVERBOSE)

[Out]

ln(48*x^3-2*x+33)

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maxima [A]  time = 0.41, size = 11, normalized size = 0.58 \begin {gather*} \log \left (48 \, x^{3} - 2 \, x + 33\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((144*x^2-2)/(48*x^3-2*x+33),x, algorithm="maxima")

[Out]

log(48*x^3 - 2*x + 33)

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mupad [B]  time = 0.06, size = 11, normalized size = 0.58 \begin {gather*} \ln \left (48\,x^3-2\,x+33\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((144*x^2 - 2)/(48*x^3 - 2*x + 33),x)

[Out]

log(48*x^3 - 2*x + 33)

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sympy [A]  time = 0.08, size = 10, normalized size = 0.53 \begin {gather*} \log {\left (48 x^{3} - 2 x + 33 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((144*x**2-2)/(48*x**3-2*x+33),x)

[Out]

log(48*x**3 - 2*x + 33)

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