3.281 \(\int \frac {f+g x^2}{\log (c (d+e x^2)^p)} \, dx\)

Optimal. Leaf size=25 \[ \text {Int}\left (\frac {f+g x^2}{\log \left (c \left (d+e x^2\right )^p\right )},x\right ) \]

[Out]

Unintegrable((g*x^2+f)/ln(c*(e*x^2+d)^p),x)

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Rubi [A]  time = 0.01, 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 = {} \[ \int \frac {f+g x^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(f + g*x^2)/Log[c*(d + e*x^2)^p],x]

[Out]

Defer[Int][(f + g*x^2)/Log[c*(d + e*x^2)^p], x]

Rubi steps

\begin {align*} \int \frac {f+g x^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx &=\int \frac {f+g x^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx\\ \end {align*}

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Mathematica [A]  time = 0.31, size = 0, normalized size = 0.00 \[ \int \frac {f+g x^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(f + g*x^2)/Log[c*(d + e*x^2)^p],x]

[Out]

Integrate[(f + g*x^2)/Log[c*(d + e*x^2)^p], x]

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fricas [A]  time = 0.96, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {g x^{2} + f}{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((g*x^2+f)/log(c*(e*x^2+d)^p),x, algorithm="fricas")

[Out]

integral((g*x^2 + f)/log((e*x^2 + d)^p*c), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((g*x^2+f)/log(c*(e*x^2+d)^p),x, algorithm="giac")

[Out]

integrate((g*x^2 + f)/log((e*x^2 + d)^p*c), x)

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maple [A]  time = 0.57, size = 0, normalized size = 0.00 \[ \int \frac {g \,x^{2}+f}{\ln \left (c \left (e \,x^{2}+d \right )^{p}\right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((g*x^2+f)/ln(c*(e*x^2+d)^p),x)

[Out]

int((g*x^2+f)/ln(c*(e*x^2+d)^p),x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {g x^{2} + f}{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((g*x^2+f)/log(c*(e*x^2+d)^p),x, algorithm="maxima")

[Out]

integrate((g*x^2 + f)/log((e*x^2 + d)^p*c), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {g\,x^2+f}{\ln \left (c\,{\left (e\,x^2+d\right )}^p\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((f + g*x^2)/log(c*(d + e*x^2)^p),x)

[Out]

int((f + g*x^2)/log(c*(d + e*x^2)^p), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {f + g x^{2}}{\log {\left (c \left (d + e x^{2}\right )^{p} \right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((g*x**2+f)/ln(c*(e*x**2+d)**p),x)

[Out]

Integral((f + g*x**2)/log(c*(d + e*x**2)**p), x)

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