3.40 \(\int (d x)^m (a+b \csc ^{-1}(c x))^2 \, dx\)

Optimal. Leaf size=19 \[ \text {Int}\left ((d x)^m \left (a+b \csc ^{-1}(c x)\right )^2,x\right ) \]

[Out]

Unintegrable((d*x)^m*(a+b*arccsc(c*x))^2,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 = {} \[ \int (d x)^m \left (a+b \csc ^{-1}(c x)\right )^2 \, dx \]

Verification is Not applicable to the result.

[In]

Int[(d*x)^m*(a + b*ArcCsc[c*x])^2,x]

[Out]

Defer[Int][(d*x)^m*(a + b*ArcCsc[c*x])^2, x]

Rubi steps

\begin {align*} \int (d x)^m \left (a+b \csc ^{-1}(c x)\right )^2 \, dx &=\int (d x)^m \left (a+b \csc ^{-1}(c x)\right )^2 \, dx\\ \end {align*}

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Mathematica [A]  time = 4.86, size = 0, normalized size = 0.00 \[ \int (d x)^m \left (a+b \csc ^{-1}(c x)\right )^2 \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(d*x)^m*(a + b*ArcCsc[c*x])^2,x]

[Out]

Integrate[(d*x)^m*(a + b*ArcCsc[c*x])^2, x]

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fricas [A]  time = 0.46, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (b^{2} \operatorname {arccsc}\left (c x\right )^{2} + 2 \, a b \operatorname {arccsc}\left (c x\right ) + a^{2}\right )} \left (d x\right )^{m}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x)^m*(a+b*arccsc(c*x))^2,x, algorithm="fricas")

[Out]

integral((b^2*arccsc(c*x)^2 + 2*a*b*arccsc(c*x) + a^2)*(d*x)^m, x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (b \operatorname {arccsc}\left (c x\right ) + a\right )}^{2} \left (d x\right )^{m}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x)^m*(a+b*arccsc(c*x))^2,x, algorithm="giac")

[Out]

integrate((b*arccsc(c*x) + a)^2*(d*x)^m, x)

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maple [A]  time = 3.97, size = 0, normalized size = 0.00 \[ \int \left (d x \right )^{m} \left (a +b \,\mathrm {arccsc}\left (c x \right )\right )^{2}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d*x)^m*(a+b*arccsc(c*x))^2,x)

[Out]

int((d*x)^m*(a+b*arccsc(c*x))^2,x)

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maxima [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x)^m*(a+b*arccsc(c*x))^2,x, algorithm="maxima")

[Out]

Timed out

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mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int {\left (d\,x\right )}^m\,{\left (a+b\,\mathrm {asin}\left (\frac {1}{c\,x}\right )\right )}^2 \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d*x)^m*(a + b*asin(1/(c*x)))^2,x)

[Out]

int((d*x)^m*(a + b*asin(1/(c*x)))^2, x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (d x\right )^{m} \left (a + b \operatorname {acsc}{\left (c x \right )}\right )^{2}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x)**m*(a+b*acsc(c*x))**2,x)

[Out]

Integral((d*x)**m*(a + b*acsc(c*x))**2, x)

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