3.957 \(\int \frac{(d+e x)^m (a+b x+c x^2)^p}{f+g x} \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.0269876, 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 = {} \[ \int \frac{(d+e x)^m \left (a+b x+c x^2\right )^p}{f+g x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 0.173333, size = 0, normalized size = 0. \[ \int \frac{(d+e x)^m \left (a+b x+c x^2\right )^p}{f+g x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 1.63, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( ex+d \right ) ^{m} \left ( c{x}^{2}+bx+a \right ) ^{p}}{gx+f}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

Timed out

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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