Optimal. Leaf size=26 \[ \frac{\text{Unintegrable}\left (\frac{1}{(c+d x) \left (a+b \sin ^{-1}(c+d x)\right )^4},x\right )}{e} \]
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Rubi [A] time = 0.0592177, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{1}{(c e+d e x) \left (a+b \sin ^{-1}(c+d x)\right )^4} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{(c e+d e x) \left (a+b \sin ^{-1}(c+d x)\right )^4} \, dx &=\frac{\operatorname{Subst}\left (\int \frac{1}{e x \left (a+b \sin ^{-1}(x)\right )^4} \, dx,x,c+d x\right )}{d}\\ &=\frac{\operatorname{Subst}\left (\int \frac{1}{x \left (a+b \sin ^{-1}(x)\right )^4} \, dx,x,c+d x\right )}{d e}\\ \end{align*}
Mathematica [A] time = 5.78724, size = 0, normalized size = 0. \[ \int \frac{1}{(c e+d e x) \left (a+b \sin ^{-1}(c+d x)\right )^4} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.521, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( dex+ce \right ) \left ( a+b\arcsin \left ( dx+c \right ) \right ) ^{4}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{a^{4} d e x + a^{4} c e +{\left (b^{4} d e x + b^{4} c e\right )} \arcsin \left (d x + c\right )^{4} + 4 \,{\left (a b^{3} d e x + a b^{3} c e\right )} \arcsin \left (d x + c\right )^{3} + 6 \,{\left (a^{2} b^{2} d e x + a^{2} b^{2} c e\right )} \arcsin \left (d x + c\right )^{2} + 4 \,{\left (a^{3} b d e x + a^{3} b c e\right )} \arcsin \left (d x + c\right )}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \frac{\int \frac{1}{a^{4} c + a^{4} d x + 4 a^{3} b c \operatorname{asin}{\left (c + d x \right )} + 4 a^{3} b d x \operatorname{asin}{\left (c + d x \right )} + 6 a^{2} b^{2} c \operatorname{asin}^{2}{\left (c + d x \right )} + 6 a^{2} b^{2} d x \operatorname{asin}^{2}{\left (c + d x \right )} + 4 a b^{3} c \operatorname{asin}^{3}{\left (c + d x \right )} + 4 a b^{3} d x \operatorname{asin}^{3}{\left (c + d x \right )} + b^{4} c \operatorname{asin}^{4}{\left (c + d x \right )} + b^{4} d x \operatorname{asin}^{4}{\left (c + d x \right )}}\, dx}{e} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (d e x + c e\right )}{\left (b \arcsin \left (d x + c\right ) + a\right )}^{4}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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