3.100.74 \(\int \frac {-17-10 x+9 x^2}{9-17 x-5 x^2+3 x^3} \, dx\)

Optimal. Leaf size=22 \[ \log \left (2 \left (3-x+x \left (2+x^2-\frac {5 (4+x)}{3}\right )\right )\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.73, number of steps used = 1, number of rules used = 1, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {1587} \begin {gather*} \log \left (3 x^3-5 x^2-17 x+9\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-17 - 10*x + 9*x^2)/(9 - 17*x - 5*x^2 + 3*x^3),x]

[Out]

Log[9 - 17*x - 5*x^2 + 3*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 (9-17 x-5 x^2+3 x^3\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 16, normalized size = 0.73 \begin {gather*} \log \left (9-17 x-5 x^2+3 x^3\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-17 - 10*x + 9*x^2)/(9 - 17*x - 5*x^2 + 3*x^3),x]

[Out]

Log[9 - 17*x - 5*x^2 + 3*x^3]

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fricas [A]  time = 0.55, size = 16, normalized size = 0.73 \begin {gather*} \log \left (3 \, x^{3} - 5 \, x^{2} - 17 \, x + 9\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((9*x^2-10*x-17)/(3*x^3-5*x^2-17*x+9),x, algorithm="fricas")

[Out]

log(3*x^3 - 5*x^2 - 17*x + 9)

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giac [A]  time = 0.18, size = 17, normalized size = 0.77 \begin {gather*} \log \left ({\left | 3 \, x^{3} - 5 \, x^{2} - 17 \, x + 9 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((9*x^2-10*x-17)/(3*x^3-5*x^2-17*x+9),x, algorithm="giac")

[Out]

log(abs(3*x^3 - 5*x^2 - 17*x + 9))

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maple [A]  time = 0.02, size = 17, normalized size = 0.77

method	result	size
derivativedivides	\(\ln \left (3 x^{3}-5 x^{2}-17 x +9\right )\)	\(17\)
default	\(\ln \left (3 x^{3}-5 x^{2}-17 x +9\right )\)	\(17\)
norman	\(\ln \left (3 x^{3}-5 x^{2}-17 x +9\right )\)	\(17\)
risch	\(\ln \left (3 x^{3}-5 x^{2}-17 x +9\right )\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((9*x^2-10*x-17)/(3*x^3-5*x^2-17*x+9),x,method=_RETURNVERBOSE)

[Out]

ln(3*x^3-5*x^2-17*x+9)

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maxima [A]  time = 0.35, size = 16, normalized size = 0.73 \begin {gather*} \log \left (3 \, x^{3} - 5 \, x^{2} - 17 \, x + 9\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((9*x^2-10*x-17)/(3*x^3-5*x^2-17*x+9),x, algorithm="maxima")

[Out]

log(3*x^3 - 5*x^2 - 17*x + 9)

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mupad [B]  time = 0.13, size = 16, normalized size = 0.73 \begin {gather*} \ln \left (3\,x^3-5\,x^2-17\,x+9\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((10*x - 9*x^2 + 17)/(17*x + 5*x^2 - 3*x^3 - 9),x)

[Out]

log(3*x^3 - 5*x^2 - 17*x + 9)

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sympy [A]  time = 0.08, size = 15, normalized size = 0.68 \begin {gather*} \log {\left (3 x^{3} - 5 x^{2} - 17 x + 9 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((9*x**2-10*x-17)/(3*x**3-5*x**2-17*x+9),x)

[Out]

log(3*x**3 - 5*x**2 - 17*x + 9)

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