3.65 \(\int \sqrt {c+d x} \csc (a+b x) \, dx\)

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

[Out]

Unintegrable(csc(b*x+a)*(d*x+c)^(1/2),x)

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Rubi [A]  time = 0.03, 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 = {} \[ \int \sqrt {c+d x} \csc (a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

Int[Sqrt[c + d*x]*Csc[a + b*x],x]

[Out]

Defer[Int][Sqrt[c + d*x]*Csc[a + b*x], x]

Rubi steps

\begin {align*} \int \sqrt {c+d x} \csc (a+b x) \, dx &=\int \sqrt {c+d x} \csc (a+b x) \, dx\\ \end {align*}

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Mathematica [A]  time = 15.91, size = 0, normalized size = 0.00 \[ \int \sqrt {c+d x} \csc (a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Sqrt[c + d*x]*Csc[a + b*x],x]

[Out]

Integrate[Sqrt[c + d*x]*Csc[a + b*x], x]

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fricas [A]  time = 0.62, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\sqrt {d x + c} \csc \left (b x + a\right ), x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csc(b*x+a)*(d*x+c)^(1/2),x, algorithm="fricas")

[Out]

integral(sqrt(d*x + c)*csc(b*x + a), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csc(b*x+a)*(d*x+c)^(1/2),x, algorithm="giac")

[Out]

integrate(sqrt(d*x + c)*csc(b*x + a), x)

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maple [A]  time = 0.09, size = 0, normalized size = 0.00 \[ \int \csc \left (b x +a \right ) \sqrt {d x +c}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csc(b*x+a)*(d*x+c)^(1/2),x, algorithm="maxima")

[Out]

integrate(sqrt(d*x + c)*csc(b*x + a), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((c + d*x)^(1/2)/sin(a + b*x),x)

[Out]

int((c + d*x)^(1/2)/sin(a + b*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csc(b*x+a)*(d*x+c)**(1/2),x)

[Out]

Integral(sqrt(c + d*x)*csc(a + b*x), x)

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