Optimal. Leaf size=29 \[ \frac {\text {Int}\left (\frac {\sqrt {a+b \sin ^{-1}(c+d x)}}{c+d x},x\right )}{e} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.08, 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 = {} \[ \int \frac {\sqrt {a+b \sin ^{-1}(c+d x)}}{c e+d e x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\sqrt {a+b \sin ^{-1}(c+d x)}}{c e+d e x} \, dx &=\frac {\operatorname {Subst}\left (\int \frac {\sqrt {a+b \sin ^{-1}(x)}}{e x} \, dx,x,c+d x\right )}{d}\\ &=\frac {\operatorname {Subst}\left (\int \frac {\sqrt {a+b \sin ^{-1}(x)}}{x} \, dx,x,c+d x\right )}{d e}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 2.65, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {a+b \sin ^{-1}(c+d x)}}{c e+d e x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {b \arcsin \left (d x + c\right ) + a}}{d e x + c e}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.25, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {a +b \arcsin \left (d x +c \right )}}{d e x +c e}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {b \arcsin \left (d x + c\right ) + a}}{d e x + c e}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {\sqrt {a+b\,\mathrm {asin}\left (c+d\,x\right )}}{c\,e+d\,e\,x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \frac {\int \frac {\sqrt {a + b \operatorname {asin}{\left (c + d x \right )}}}{c + d x}\, dx}{e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________