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

Optimal. Leaf size=15 \[ \text {Int}\left (\frac {x}{a+b \csc ^{-1}(c x)},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.02, 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 = {} \[ \int \frac {x}{a+b \csc ^{-1}(c x)} \, dx \]

Verification is Not applicable to the result.

[In]

Int[x/(a + b*ArcCsc[c*x]),x]

[Out]

Defer[Int][x/(a + b*ArcCsc[c*x]), x]

Rubi steps

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

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Mathematica [A]  time = 2.91, size = 0, normalized size = 0.00 \[ \int \frac {x}{a+b \csc ^{-1}(c x)} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[x/(a + b*ArcCsc[c*x]),x]

[Out]

Integrate[x/(a + b*ArcCsc[c*x]), x]

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fricas [A]  time = 1.84, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {x}{b \operatorname {arccsc}\left (c x\right ) + a}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(x/(b*arccsc(c*x) + a), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x/(b*arccsc(c*x) + a), x)

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maple [A]  time = 2.29, size = 0, normalized size = 0.00 \[ \int \frac {x}{a +b \,\mathrm {arccsc}\left (c x \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x/(b*arccsc(c*x) + a), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.07 \[ \int \frac {x}{a+b\,\mathrm {asin}\left (\frac {1}{c\,x}\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x/(a + b*asin(1/(c*x))),x)

[Out]

int(x/(a + b*asin(1/(c*x))), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(x/(a + b*acsc(c*x)), x)

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