3.37.25 \(\int -\frac {64 x^3}{-715+16 x^4} \, dx\)

Optimal. Leaf size=12 \[ \log \left (\frac {5}{-\frac {715}{16}+x^4}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.83, number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 260} \begin {gather*} -\log \left (715-16 x^4\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-64*x^3)/(-715 + 16*x^4),x]

[Out]

-Log[715 - 16*x^4]

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 260

Int[(x_)^(m_.)/((a_) + (b_.)*(x_)^(n_)), x_Symbol] :> Simp[Log[RemoveContent[a + b*x^n, x]]/(b*n), x] /; FreeQ
[{a, b, m, n}, x] && EqQ[m, n - 1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\left (64 \int \frac {x^3}{-715+16 x^4} \, dx\right )\\ &=-\log \left (715-16 x^4\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.83 \begin {gather*} -\log \left (715-16 x^4\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-64*x^3)/(-715 + 16*x^4),x]

[Out]

-Log[715 - 16*x^4]

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fricas [A]  time = 0.54, size = 10, normalized size = 0.83 \begin {gather*} -\log \left (16 \, x^{4} - 715\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-64*x^3/(16*x^4-715),x, algorithm="fricas")

[Out]

-log(16*x^4 - 715)

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giac [A]  time = 0.21, size = 11, normalized size = 0.92 \begin {gather*} -\log \left ({\left | 16 \, x^{4} - 715 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-64*x^3/(16*x^4-715),x, algorithm="giac")

[Out]

-log(abs(16*x^4 - 715))

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maple [A]  time = 0.09, size = 11, normalized size = 0.92

method	result	size
derivativedivides	\(-\ln \left (16 x^{4}-715\right )\)	\(11\)
default	\(-\ln \left (16 x^{4}-715\right )\)	\(11\)
norman	\(-\ln \left (16 x^{4}-715\right )\)	\(11\)
meijerg	\(-\ln \left (1-\frac {16 x^{4}}{715}\right )\)	\(11\)
risch	\(-\ln \left (16 x^{4}-715\right )\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-64*x^3/(16*x^4-715),x,method=_RETURNVERBOSE)

[Out]

-ln(16*x^4-715)

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maxima [A]  time = 0.44, size = 10, normalized size = 0.83 \begin {gather*} -\log \left (16 \, x^{4} - 715\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-64*x^3/(16*x^4-715),x, algorithm="maxima")

[Out]

-log(16*x^4 - 715)

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mupad [B]  time = 0.05, size = 8, normalized size = 0.67 \begin {gather*} -\ln \left (x^4-\frac {715}{16}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(64*x^3)/(16*x^4 - 715),x)

[Out]

-log(x^4 - 715/16)

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sympy [A]  time = 0.08, size = 8, normalized size = 0.67 \begin {gather*} - \log {\left (16 x^{4} - 715 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-64*x**3/(16*x**4-715),x)

[Out]

-log(16*x**4 - 715)

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