Optimal. Leaf size=9 \[ \frac {\text {Ci}\left (\sin ^{-1}(a x)\right )}{a} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {4623, 3302} \[ \frac {\text {CosIntegral}\left (\sin ^{-1}(a x)\right )}{a} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 3302
Rule 4623
Rubi steps
\begin {align*} \int \frac {1}{\sin ^{-1}(a x)} \, dx &=\frac {\operatorname {Subst}\left (\int \frac {\cos (x)}{x} \, dx,x,\sin ^{-1}(a x)\right )}{a}\\ &=\frac {\text {Ci}\left (\sin ^{-1}(a x)\right )}{a}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 9, normalized size = 1.00 \[ \frac {\text {Ci}\left (\sin ^{-1}(a x)\right )}{a} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [F] time = 0.55, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{\arcsin \left (a x\right )}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.18, size = 9, normalized size = 1.00 \[ \frac {\operatorname {Ci}\left (\arcsin \left (a x\right )\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 10, normalized size = 1.11 \[ \frac {\Ci \left (\arcsin \left (a x \right )\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\arcsin \left (a x\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.11 \[ \int \frac {1}{\mathrm {asin}\left (a\,x\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\operatorname {asin}{\left (a x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________