Optimal. Leaf size=27 \[ \frac {\text {Int}\left (\frac {1}{(c+d x) \left (a+b \sin ^{-1}(c+d x)\right )^4},x\right )}{e} \]
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Rubi [A] time = 0.06, 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 = {} \[ \int \frac {1}{(c e+d e x) \left (a+b \sin ^{-1}(c+d x)\right )^4} \, dx \]
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*}
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Mathematica [A] time = 6.49, size = 0, normalized size = 0.00 \[ \int \frac {1}{(c e+d e x) \left (a+b \sin ^{-1}(c+d x)\right )^4} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.47, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{a^{4} d e x + a^{4} c e + {\left (b^{4} d e x + b^{4} c e\right )} \arcsin \left (d x + c\right )^{4} + 4 \, {\left (a b^{3} d e x + a b^{3} c e\right )} \arcsin \left (d x + c\right )^{3} + 6 \, {\left (a^{2} b^{2} d e x + a^{2} b^{2} c e\right )} \arcsin \left (d x + c\right )^{2} + 4 \, {\left (a^{3} b d e x + a^{3} b c e\right )} \arcsin \left (d x + c\right )}, x\right ) \]
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 \[ \int \frac {1}{{\left (d e x + c e\right )} {\left (b \arcsin \left (d x + c\right ) + a\right )}^{4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.88, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (d e x +c e \right ) \left (a +b \arcsin \left (d x +c \right )\right )^{4}}\, dx \]
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 = -0.04 \[ \int \frac {1}{\left (c\,e+d\,e\,x\right )\,{\left (a+b\,\mathrm {asin}\left (c+d\,x\right )\right )}^4} \,d x \]
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 \[ \frac {\int \frac {1}{a^{4} c + a^{4} d x + 4 a^{3} b c \operatorname {asin}{\left (c + d x \right )} + 4 a^{3} b d x \operatorname {asin}{\left (c + d x \right )} + 6 a^{2} b^{2} c \operatorname {asin}^{2}{\left (c + d x \right )} + 6 a^{2} b^{2} d x \operatorname {asin}^{2}{\left (c + d x \right )} + 4 a b^{3} c \operatorname {asin}^{3}{\left (c + d x \right )} + 4 a b^{3} d x \operatorname {asin}^{3}{\left (c + d x \right )} + b^{4} c \operatorname {asin}^{4}{\left (c + d x \right )} + b^{4} d x \operatorname {asin}^{4}{\left (c + d x \right )}}\, dx}{e} \]
Verification of antiderivative is not currently implemented for this CAS.
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