3.75 \(\int (a+b (F^{g (e+f x)})^n)^p (c+d x)^m \, dx\)

Optimal. Leaf size=28 \[ \text{Unintegrable}\left ((c+d x)^m \left (a+b \left (F^{e g+f g x}\right )^n\right )^p,x\right ) \]

[Out]

Unintegrable[(a + b*(F^(e*g + f*g*x))^n)^p*(c + d*x)^m, x]

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Rubi [A]  time = 0.118741, 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 = {} \[ \int \left (a+b \left (F^{g (e+f x)}\right )^n\right )^p (c+d x)^m \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 0.264622, size = 0, normalized size = 0. \[ \int \left (a+b \left (F^{g (e+f x)}\right )^n\right )^p (c+d x)^m \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.184, size = 0, normalized size = 0. \begin{align*} \int \left ( a+b \left ({F}^{g \left ( fx+e \right ) } \right ) ^{n} \right ) ^{p} \left ( dx+c \right ) ^{m}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a+b*(F^(g*(f*x+e)))^n)^p*(d*x+c)^m,x)

[Out]

int((a+b*(F^(g*(f*x+e)))^n)^p*(d*x+c)^m,x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(((F^((f*x + e)*g))^n*b + a)^p*(d*x + c)^m, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(((F^(f*g*x + e*g))^n*b + a)^p*(d*x + c)^m, x)

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*(F**(g*(f*x+e)))**n)**p*(d*x+c)**m,x)

[Out]

Timed out

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(((F^((f*x + e)*g))^n*b + a)^p*(d*x + c)^m, x)