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

Optimal. Leaf size=29 \[ \text {Int}\left ((c+d x)^m \left (a+b \left (F^{e g+f g x}\right )^n\right )^p,x\right ) \]

[Out]

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

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Rubi [A]  time = 0.12, 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 = {} \[ \int \left (a+b \left (F^{g (e+f x)}\right )^n\right )^p (c+d x)^m \, dx \]

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*}

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Mathematica [A]  time = 0.29, size = 0, normalized size = 0.00 \[ \int \left (a+b \left (F^{g (e+f x)}\right )^n\right )^p (c+d x)^m \, dx \]

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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fricas [A]  time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left ({\left (F^{f g x + e g}\right )}^{n} b + a\right )}^{p} {\left (d x + c\right )}^{m}, x\right ) \]

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

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)

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maple [A]  time = 0.21, size = 0, normalized size = 0.00 \[ \int \left (b \left (F^{\left (f x +e \right ) g}\right )^{n}+a \right )^{p} \left (d x +c \right )^{m}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.03 \[ \int {\left (a+b\,{\left (F^{g\,\left (e+f\,x\right )}\right )}^n\right )}^p\,{\left (c+d\,x\right )}^m \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

Timed out

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