3.1.74 \(\int \frac {(c+d x)^m}{(a+b (F^{g (e+f x)})^n)^2} \, dx\) [74]

Optimal. Leaf size=29 \[ \text {Int}\left (\frac {(c+d x)^m}{\left (a+b \left (F^{e g+f g x}\right )^n\right )^2},x\right ) \]

[Out]

Unintegrable((d*x+c)^m/(a+b*(F^(f*g*x+e*g))^n)^2,x)

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Rubi [A]
time = 0.08, 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 = {} \begin {gather*} \int \frac {(c+d x)^m}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 0.21, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(c+d x)^m}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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Maple [A]
time = 0.01, size = 0, normalized size = 0.00 \[\int \frac {\left (d x +c \right )^{m}}{\left (a +b \left (F^{g \left (f x +e \right )}\right )^{n}\right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral((d*x + c)^m/(2*(F^(f*g*x + g*e))^n*a*b + (F^(f*g*x + g*e))^(2*n)*b^2 + a^2), x)

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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\left (c+d\,x\right )}^m}{{\left (a+b\,{\left (F^{g\,\left (e+f\,x\right )}\right )}^n\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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