3.1.34 \(\int \frac {1}{a+b \csc ^{-1}(c x)} \, dx\) [34]

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)

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Rubi [A]
time = 0.00, 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 = {} \begin {gather*} \int \frac {1}{a+b \csc ^{-1}(c x)} \, dx \end {gather*}

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*}

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Mathematica [A]
time = 2.41, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{a+b \csc ^{-1}(c x)} \, dx \end {gather*}

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]

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Maple [A]
time = 0.91, 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)

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

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)

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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)

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

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)

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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)

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

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)

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