3.30 \(\int F^{c (a+b x)} (f x)^m \csc ^2(d+e x) \, dx\)

Optimal. Leaf size=26 \[ \text{CannotIntegrate}\left ((f x)^m \csc ^2(d+e x) F^{a c+b c x},x\right ) \]

[Out]

CannotIntegrate[F^(a*c + b*c*x)*(f*x)^m*Csc[d + e*x]^2, x]

________________________________________________________________________________________

Rubi [A]  time = 0.951491, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int F^{c (a+b x)} (f x)^m \csc ^2(d+e x) \, dx \]

Verification is Not applicable to the result.

[In]

Int[F^(c*(a + b*x))*(f*x)^m*Csc[d + e*x]^2,x]

[Out]

Defer[Int][F^(a*c + b*c*x)*(f*x)^m*Csc[d + e*x]^2, x]

Rubi steps

\begin{align*} \int F^{c (a+b x)} (f x)^m \csc ^2(d+e x) \, dx &=\int F^{a c+b c x} (f x)^m \csc ^2(d+e x) \, dx\\ \end{align*}

Mathematica [A]  time = 10.6327, size = 0, normalized size = 0. \[ \int F^{c (a+b x)} (f x)^m \csc ^2(d+e x) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[F^(c*(a + b*x))*(f*x)^m*Csc[d + e*x]^2,x]

[Out]

Integrate[F^(c*(a + b*x))*(f*x)^m*Csc[d + e*x]^2, x]

________________________________________________________________________________________

Maple [A]  time = 0.071, size = 0, normalized size = 0. \begin{align*} \int{\frac{{F}^{c \left ( bx+a \right ) } \left ( fx \right ) ^{m}}{ \left ( \sin \left ( ex+d \right ) \right ) ^{2}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F^(c*(b*x+a))*(f*x)^m/sin(e*x+d)^2,x)

[Out]

int(F^(c*(b*x+a))*(f*x)^m/sin(e*x+d)^2,x)

________________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (f x\right )^{m} F^{{\left (b x + a\right )} c}}{\sin \left (e x + d\right )^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F^(c*(b*x+a))*(f*x)^m/sin(e*x+d)^2,x, algorithm="maxima")

[Out]

integrate((f*x)^m*F^((b*x + a)*c)/sin(e*x + d)^2, x)

________________________________________________________________________________________

Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (-\frac{\left (f x\right )^{m} F^{b c x + a c}}{\cos \left (e x + d\right )^{2} - 1}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F^(c*(b*x+a))*(f*x)^m/sin(e*x+d)^2,x, algorithm="fricas")

[Out]

integral(-(f*x)^m*F^(b*c*x + a*c)/(cos(e*x + d)^2 - 1), x)

________________________________________________________________________________________

Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{F^{c \left (a + b x\right )} \left (f x\right )^{m}}{\sin ^{2}{\left (d + e x \right )}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F**(c*(b*x+a))*(f*x)**m/sin(e*x+d)**2,x)

[Out]

Integral(F**(c*(a + b*x))*(f*x)**m/sin(d + e*x)**2, x)

________________________________________________________________________________________

Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (f x\right )^{m} F^{{\left (b x + a\right )} c}}{\sin \left (e x + d\right )^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F^(c*(b*x+a))*(f*x)^m/sin(e*x+d)^2,x, algorithm="giac")

[Out]

integrate((f*x)^m*F^((b*x + a)*c)/sin(e*x + d)^2, x)