3.34 \(\int \frac {1}{a+b \csc ^{-1}(c x)} \, dx\)

Optimal. Leaf size=13 \[ \text {Int}\left (\frac {1}{a+b \csc ^{-1}(c x)},x\right ) \]

[Out]

Unintegrable(1/(a+b*arccsc(c*x)),x)

________________________________________________________________________________________

Rubi [A]  time = 0.01, 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 = {} \[ \int \frac {1}{a+b \csc ^{-1}(c x)} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(a + b*ArcCsc[c*x])^(-1),x]

[Out]

Defer[Int][(a + b*ArcCsc[c*x])^(-1), x]

Rubi steps

\begin {align*} \int \frac {1}{a+b \csc ^{-1}(c x)} \, dx &=\int \frac {1}{a+b \csc ^{-1}(c x)} \, dx\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 3.49, size = 0, normalized size = 0.00 \[ \int \frac {1}{a+b \csc ^{-1}(c x)} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(a + b*ArcCsc[c*x])^(-1),x]

[Out]

Integrate[(a + b*ArcCsc[c*x])^(-1), x]

________________________________________________________________________________________

fricas [A]  time = 1.08, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{b \operatorname {arccsc}\left (c x\right ) + a}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a+b*arccsc(c*x)),x, algorithm="fricas")

[Out]

integral(1/(b*arccsc(c*x) + a), x)

________________________________________________________________________________________

giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{b \operatorname {arccsc}\left (c x\right ) + a}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a+b*arccsc(c*x)),x, algorithm="giac")

[Out]

integrate(1/(b*arccsc(c*x) + a), x)

________________________________________________________________________________________

maple [A]  time = 0.90, size = 0, normalized size = 0.00 \[ \int \frac {1}{a +b \,\mathrm {arccsc}\left (c x \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(a+b*arccsc(c*x)),x)

[Out]

int(1/(a+b*arccsc(c*x)),x)

________________________________________________________________________________________

maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{b \operatorname {arccsc}\left (c x\right ) + a}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a+b*arccsc(c*x)),x, algorithm="maxima")

[Out]

integrate(1/(b*arccsc(c*x) + a), x)

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.08 \[ \int \frac {1}{a+b\,\mathrm {asin}\left (\frac {1}{c\,x}\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(a + b*asin(1/(c*x))),x)

[Out]

int(1/(a + b*asin(1/(c*x))), x)

________________________________________________________________________________________

sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{a + b \operatorname {acsc}{\left (c x \right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a+b*acsc(c*x)),x)

[Out]

Integral(1/(a + b*acsc(c*x)), x)

________________________________________________________________________________________