3.284 \(\int x^m \csc ^3(a+b x) \sec ^2(a+b x) \, dx\)

Optimal. Leaf size=23 \[ \text {Int}\left (x^m \csc ^3(a+b x) \sec ^2(a+b x),x\right ) \]

[Out]

CannotIntegrate(x^m*csc(b*x+a)^3*sec(b*x+a)^2,x)

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Rubi [A]  time = 0.92, 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 = {} \[ \int x^m \csc ^3(a+b x) \sec ^2(a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

Int[x^m*Csc[a + b*x]^3*Sec[a + b*x]^2,x]

[Out]

Defer[Int][x^m*Csc[a + b*x]^3*Sec[a + b*x]^2, x]

Rubi steps

\begin {align*} \int x^m \csc ^3(a+b x) \sec ^2(a+b x) \, dx &=\int x^m \csc ^3(a+b x) \sec ^2(a+b x) \, dx\\ \end {align*}

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Mathematica [A]  time = 39.65, size = 0, normalized size = 0.00 \[ \int x^m \csc ^3(a+b x) \sec ^2(a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[x^m*Csc[a + b*x]^3*Sec[a + b*x]^2,x]

[Out]

Integrate[x^m*Csc[a + b*x]^3*Sec[a + b*x]^2, x]

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fricas [A]  time = 0.45, size = 0, normalized size = 0.00 \[ {\rm integral}\left (x^{m} \csc \left (b x + a\right )^{3} \sec \left (b x + a\right )^{2}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm="fricas")

[Out]

integral(x^m*csc(b*x + a)^3*sec(b*x + a)^2, x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int x^{m} \csc \left (b x + a\right )^{3} \sec \left (b x + a\right )^{2}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm="giac")

[Out]

integrate(x^m*csc(b*x + a)^3*sec(b*x + a)^2, x)

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maple [A]  time = 0.11, size = 0, normalized size = 0.00 \[ \int x^{m} \left (\csc ^{3}\left (b x +a \right )\right ) \left (\sec ^{2}\left (b x +a \right )\right )\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^m*csc(b*x+a)^3*sec(b*x+a)^2,x)

[Out]

int(x^m*csc(b*x+a)^3*sec(b*x+a)^2,x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int x^{m} \csc \left (b x + a\right )^{3} \sec \left (b x + a\right )^{2}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm="maxima")

[Out]

integrate(x^m*csc(b*x + a)^3*sec(b*x + a)^2, x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {x^m}{{\cos \left (a+b\,x\right )}^2\,{\sin \left (a+b\,x\right )}^3} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^m/(cos(a + b*x)^2*sin(a + b*x)^3),x)

[Out]

int(x^m/(cos(a + b*x)^2*sin(a + b*x)^3), x)

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sympy [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(x**m*csc(b*x+a)**3*sec(b*x+a)**2,x)

[Out]

Timed out

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