3.29 \(\int F^{c (a+b x)} (f x)^m \csc (d+e x) \, dx\)

Optimal. Leaf size=25 \[ \text {Int}\left ((f x)^m \csc (d+e x) F^{a c+b c x},x\right ) \]

[Out]

CannotIntegrate(F^(b*c*x+a*c)*(f*x)^m*csc(e*x+d),x)

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Rubi [A]  time = 0.62, 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 = {} \[ \int F^{c (a+b x)} (f x)^m \csc (d+e x) \, dx \]

Verification is Not applicable to the result.

[In]

Int[F^(c*(a + b*x))*(f*x)^m*Csc[d + e*x],x]

[Out]

Defer[Int][F^(a*c + b*c*x)*(f*x)^m*Csc[d + e*x], x]

Rubi steps

\begin {align*} \int F^{c (a+b x)} (f x)^m \csc (d+e x) \, dx &=\int F^{a c+b c x} (f x)^m \csc (d+e x) \, dx\\ \end {align*}

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Mathematica [A]  time = 9.20, size = 0, normalized size = 0.00 \[ \int F^{c (a+b x)} (f x)^m \csc (d+e x) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[F^(c*(a + b*x))*(f*x)^m*Csc[d + e*x],x]

[Out]

Integrate[F^(c*(a + b*x))*(f*x)^m*Csc[d + e*x], x]

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fricas [A]  time = 1.48, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\left (f x\right )^{m} F^{b c x + a c}}{\sin \left (e x + d\right )}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F^(c*(b*x+a))*(f*x)^m/sin(e*x+d),x, algorithm="fricas")

[Out]

integral((f*x)^m*F^(b*c*x + a*c)/sin(e*x + d), x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (f x\right )^{m} F^{{\left (b x + a\right )} c}}{\sin \left (e x + d\right )}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F^(c*(b*x+a))*(f*x)^m/sin(e*x+d),x, algorithm="giac")

[Out]

integrate((f*x)^m*F^((b*x + a)*c)/sin(e*x + d), x)

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maple [A]  time = 0.15, size = 0, normalized size = 0.00 \[ \int \frac {F^{c \left (b x +a \right )} \left (f x \right )^{m}}{\sin \left (e x +d \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F^(c*(b*x+a))*(f*x)^m/sin(e*x+d),x)

[Out]

int(F^(c*(b*x+a))*(f*x)^m/sin(e*x+d),x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (f x\right )^{m} F^{{\left (b x + a\right )} c}}{\sin \left (e x + d\right )}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F^(c*(b*x+a))*(f*x)^m/sin(e*x+d),x, algorithm="maxima")

[Out]

integrate((f*x)^m*F^((b*x + a)*c)/sin(e*x + d), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((F^(c*(a + b*x))*(f*x)^m)/sin(d + e*x),x)

[Out]

int((F^(c*(a + b*x))*(f*x)^m)/sin(d + e*x), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {F^{c \left (a + b x\right )} \left (f x\right )^{m}}{\sin {\left (d + e x \right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F**(c*(b*x+a))*(f*x)**m/sin(e*x+d),x)

[Out]

Integral(F**(c*(a + b*x))*(f*x)**m/sin(d + e*x), x)

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