3.118 \(\int \frac {1}{x \log ^3(c (a+b x^2)^p)} \, dx\)

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {1}{x \log ^3\left (c \left (a+b x^2\right )^p\right )},x\right ) \]

[Out]

Unintegrable(1/x/ln(c*(b*x^2+a)^p)^3,x)

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Rubi [A]  time = 0.02, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {1}{x \log ^3\left (c \left (a+b x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x*Log[c*(a + b*x^2)^p]^3),x]

[Out]

Defer[Int][1/(x*Log[c*(a + b*x^2)^p]^3), x]

Rubi steps

\begin {align*} \int \frac {1}{x \log ^3\left (c \left (a+b x^2\right )^p\right )} \, dx &=\int \frac {1}{x \log ^3\left (c \left (a+b x^2\right )^p\right )} \, dx\\ \end {align*}

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Mathematica [A]  time = 0.59, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \log ^3\left (c \left (a+b x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x*Log[c*(a + b*x^2)^p]^3),x]

[Out]

Integrate[1/(x*Log[c*(a + b*x^2)^p]^3), x]

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fricas [A]  time = 0.45, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{x \log \left ({\left (b x^{2} + a\right )}^{p} c\right )^{3}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/log(c*(b*x^2+a)^p)^3,x, algorithm="fricas")

[Out]

integral(1/(x*log((b*x^2 + a)^p*c)^3), x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \log \left ({\left (b x^{2} + a\right )}^{p} c\right )^{3}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/log(c*(b*x^2+a)^p)^3,x, algorithm="giac")

[Out]

integrate(1/(x*log((b*x^2 + a)^p*c)^3), x)

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maple [A]  time = 3.74, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \ln \left (c \left (b \,x^{2}+a \right )^{p}\right )^{3}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x/ln(c*(b*x^2+a)^p)^3,x)

[Out]

int(1/x/ln(c*(b*x^2+a)^p)^3,x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {b^{2} p x^{4} + a b {\left (p - \log \relax (c)\right )} x^{2} - a^{2} \log \relax (c) - {\left (a b p x^{2} + a^{2} p\right )} \log \left (b x^{2} + a\right )}{4 \, {\left (b^{2} p^{4} x^{4} \log \left (b x^{2} + a\right )^{2} + 2 \, b^{2} p^{3} x^{4} \log \left (b x^{2} + a\right ) \log \relax (c) + b^{2} p^{2} x^{4} \log \relax (c)^{2}\right )}} + \int \frac {a b x^{2} + 2 \, a^{2}}{2 \, {\left (b^{2} p^{3} x^{5} \log \left (b x^{2} + a\right ) + b^{2} p^{2} x^{5} \log \relax (c)\right )}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/log(c*(b*x^2+a)^p)^3,x, algorithm="maxima")

[Out]

-1/4*(b^2*p*x^4 + a*b*(p - log(c))*x^2 - a^2*log(c) - (a*b*p*x^2 + a^2*p)*log(b*x^2 + a))/(b^2*p^4*x^4*log(b*x
^2 + a)^2 + 2*b^2*p^3*x^4*log(b*x^2 + a)*log(c) + b^2*p^2*x^4*log(c)^2) + integrate(1/2*(a*b*x^2 + 2*a^2)/(b^2
*p^3*x^5*log(b*x^2 + a) + b^2*p^2*x^5*log(c)), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {1}{x\,{\ln \left (c\,{\left (b\,x^2+a\right )}^p\right )}^3} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x*log(c*(a + b*x^2)^p)^3),x)

[Out]

int(1/(x*log(c*(a + b*x^2)^p)^3), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \log {\left (c \left (a + b x^{2}\right )^{p} \right )}^{3}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/ln(c*(b*x**2+a)**p)**3,x)

[Out]

Integral(1/(x*log(c*(a + b*x**2)**p)**3), x)

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