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

Optimal. Leaf size=31 \[ \text{CannotIntegrate}\left (\frac{(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0075481, 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 = {} \[ \int \frac{(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 0.25432, size = 0, normalized size = 0. \[ \int \frac{(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.157, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( bx+a \right ) ^{m} \left ( dx+c \right ) ^{n} \left ( fx+e \right ) ^{p}}{hx+g}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

Timed out

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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