3.130 \(\int \frac {(d x)^m}{a+b \tan ^{-1}(c x^3)} \, dx\)

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {(d x)^m}{a+b \tan ^{-1}\left (c x^3\right )},x\right ) \]

[Out]

Unintegrable((d*x)^m/(a+b*arctan(c*x^3)),x)

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Rubi [A]  time = 0.03, 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 = {} \[ \int \frac {(d x)^m}{a+b \tan ^{-1}\left (c x^3\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(d*x)^m/(a + b*ArcTan[c*x^3]),x]

[Out]

Defer[Int][(d*x)^m/(a + b*ArcTan[c*x^3]), x]

Rubi steps

\begin {align*} \int \frac {(d x)^m}{a+b \tan ^{-1}\left (c x^3\right )} \, dx &=\int \frac {(d x)^m}{a+b \tan ^{-1}\left (c x^3\right )} \, dx\\ \end {align*}

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Mathematica [A]  time = 0.34, size = 0, normalized size = 0.00 \[ \int \frac {(d x)^m}{a+b \tan ^{-1}\left (c x^3\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(d*x)^m/(a + b*ArcTan[c*x^3]),x]

[Out]

Integrate[(d*x)^m/(a + b*ArcTan[c*x^3]), x]

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fricas [A]  time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\left (d x\right )^{m}}{b \arctan \left (c x^{3}\right ) + a}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x)^m/(a+b*arctan(c*x^3)),x, algorithm="fricas")

[Out]

integral((d*x)^m/(b*arctan(c*x^3) + a), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x)^m/(a+b*arctan(c*x^3)),x, algorithm="giac")

[Out]

integrate((d*x)^m/(b*arctan(c*x^3) + a), x)

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maple [A]  time = 0.15, size = 0, normalized size = 0.00 \[ \int \frac {\left (d x \right )^{m}}{a +b \arctan \left (c \,x^{3}\right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d*x)^m/(a+b*arctan(c*x^3)),x)

[Out]

int((d*x)^m/(a+b*arctan(c*x^3)),x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (d x\right )^{m}}{b \arctan \left (c x^{3}\right ) + a}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x)^m/(a+b*arctan(c*x^3)),x, algorithm="maxima")

[Out]

integrate((d*x)^m/(b*arctan(c*x^3) + a), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d*x)^m/(a + b*atan(c*x^3)),x)

[Out]

int((d*x)^m/(a + b*atan(c*x^3)), x)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x)**m/(a+b*atan(c*x**3)),x)

[Out]

Timed out

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