Optimal. Leaf size=38 \[ \text {Int}\left (\frac {\log \left (h (f+g x)^m\right )}{\sqrt {1-c^2 x^2} \left (a+b \cos ^{-1}(c x)\right )},x\right ) \]
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Rubi [A] time = 0.20, 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 = {} \[ \int \frac {\log \left (h (f+g x)^m\right )}{\sqrt {1-c^2 x^2} \left (a+b \cos ^{-1}(c x)\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\log \left (h (f+g x)^m\right )}{\sqrt {1-c^2 x^2} \left (a+b \cos ^{-1}(c x)\right )} \, dx &=\int \frac {\log \left (h (f+g x)^m\right )}{\sqrt {1-c^2 x^2} \left (a+b \cos ^{-1}(c x)\right )} \, dx\\ \end {align*}
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Mathematica [A] time = 0.20, size = 0, normalized size = 0.00 \[ \int \frac {\log \left (h (f+g x)^m\right )}{\sqrt {1-c^2 x^2} \left (a+b \cos ^{-1}(c x)\right )} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.57, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {\sqrt {-c^{2} x^{2} + 1} \log \left ({\left (g x + f\right )}^{m} h\right )}{a c^{2} x^{2} + {\left (b c^{2} x^{2} - b\right )} \arccos \left (c x\right ) - a}, x\right ) \]
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 \[ \int \frac {\log \left ({\left (g x + f\right )}^{m} h\right )}{\sqrt {-c^{2} x^{2} + 1} {\left (b \arccos \left (c x\right ) + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 7.59, size = 0, normalized size = 0.00 \[ \int \frac {\ln \left (h \left (g x +f \right )^{m}\right )}{\left (a +b \arccos \left (c x \right )\right ) \sqrt {-c^{2} x^{2}+1}}\, dx \]
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 \[ \int \frac {\log \left ({\left (g x + f\right )}^{m} h\right )}{\sqrt {-c^{2} x^{2} + 1} {\left (b \arccos \left (c x\right ) + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {\ln \left (h\,{\left (f+g\,x\right )}^m\right )}{\left (a+b\,\mathrm {acos}\left (c\,x\right )\right )\,\sqrt {1-c^2\,x^2}} \,d x \]
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 \[ \int \frac {\log {\left (h \left (f + g x\right )^{m} \right )}}{\sqrt {- \left (c x - 1\right ) \left (c x + 1\right )} \left (a + b \operatorname {acos}{\left (c x \right )}\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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