Optimal. Leaf size=17 \[ \text {Int}\left (\frac {\text {ArcCos}(a x)^n}{\sqrt {b x}},x\right ) \]
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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 = {}
\begin {gather*} \int \frac {\text {ArcCos}(a x)^n}{\sqrt {b x}} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\cos ^{-1}(a x)^n}{\sqrt {b x}} \, dx &=\int \frac {\cos ^{-1}(a x)^n}{\sqrt {b x}} \, dx\\ \end {align*}
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Mathematica [A]
time = 1.22, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\text {ArcCos}(a x)^n}{\sqrt {b x}} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.14, size = 0, normalized size = 0.00 \[\int \frac {\arccos \left (a x \right )^{n}}{\sqrt {b x}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \frac {\operatorname {acos}^{n}{\left (a x \right )}}{\sqrt {b x}}\, dx \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [A]
time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int \frac {{\mathrm {acos}\left (a\,x\right )}^n}{\sqrt {b\,x}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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