Optimal. Leaf size=13 \[ \text {Int}\left (\frac {1}{x \cos ^{-1}(a x)^4},x\right ) \]
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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 = {} \[ \int \frac {1}{x \cos ^{-1}(a x)^4} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{x \cos ^{-1}(a x)^4} \, dx &=\int \frac {1}{x \cos ^{-1}(a x)^4} \, dx\\ \end {align*}
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Mathematica [A] time = 3.05, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \cos ^{-1}(a x)^4} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.49, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{x \arccos \left (a x\right )^{4}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \arccos \left (a x\right )^{4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.21, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \arccos \left (a x \right )^{4}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \frac {2 \, a^{3} x^{3} \arctan \left (\sqrt {a x + 1} \sqrt {-a x + 1}, a x\right )^{3} \int \frac {{\left (2 \, a^{2} x^{2} - 3\right )} \sqrt {a x + 1} \sqrt {-a x + 1}}{{\left (a^{5} x^{6} - a^{3} x^{4}\right )} \arctan \left (\sqrt {a x + 1} \sqrt {-a x + 1}, a x\right )}\,{d x} + a x \arctan \left (\sqrt {a x + 1} \sqrt {-a x + 1}, a x\right ) + 2 \, {\left (a^{2} x^{2} + \arctan \left (\sqrt {a x + 1} \sqrt {-a x + 1}, a x\right )^{2}\right )} \sqrt {a x + 1} \sqrt {-a x + 1}}{6 \, a^{3} x^{3} \arctan \left (\sqrt {a x + 1} \sqrt {-a x + 1}, a x\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.08 \[ \int \frac {1}{x\,{\mathrm {acos}\left (a\,x\right )}^4} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \operatorname {acos}^{4}{\left (a x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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