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

Optimal. Leaf size=32 \[ \text {Int}\left (\frac {(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.01, 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 = {} \[ \int \frac {(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx \]

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*}

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Mathematica [A]  time = 0.25, size = 0, normalized size = 0.00 \[ \int \frac {(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx \]

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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fricas [A]  time = 0.81, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (b x + a\right )}^{m} {\left (d x + c\right )}^{n} {\left (f x + e\right )}^{p}}{h x + g}, x\right ) \]

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

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)

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maple [A]  time = 0.26, size = 0, normalized size = 0.00 \[ \int \frac {\left (b x +a \right )^{m} \left (d x +c \right )^{n} \left (f x +e \right )^{p}}{h x +g}\, dx \]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

Timed out

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