Optimal. Leaf size=65 \[ \frac {4 a \text {Int}\left (\frac {\cos ^{-1}(a x)^3 (b x)^{m+1}}{\sqrt {1-a^2 x^2}},x\right )}{b (m+1)}+\frac {\cos ^{-1}(a x)^4 (b x)^{m+1}}{b (m+1)} \]
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Rubi [A] time = 0.12, 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 = {} \[ \int (b x)^m \cos ^{-1}(a x)^4 \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int (b x)^m \cos ^{-1}(a x)^4 \, dx &=\frac {(b x)^{1+m} \cos ^{-1}(a x)^4}{b (1+m)}+\frac {(4 a) \int \frac {(b x)^{1+m} \cos ^{-1}(a x)^3}{\sqrt {1-a^2 x^2}} \, dx}{b (1+m)}\\ \end {align*}
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Mathematica [A] time = 1.30, size = 0, normalized size = 0.00 \[ \int (b x)^m \cos ^{-1}(a x)^4 \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.61, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\left (b x\right )^{m} \arccos \left (a x\right )^{4}, x\right ) \]
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 \[ \int \left (b x\right )^{m} \arccos \left (a x\right )^{4}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.12, size = 0, normalized size = 0.00 \[ \int \left (b x \right )^{m} \arccos \left (a x \right )^{4}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.02 \[ \int {\mathrm {acos}\left (a\,x\right )}^4\,{\left (b\,x\right )}^m \,d x \]
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 \[ \int \left (b x\right )^{m} \operatorname {acos}^{4}{\left (a x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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