Optimal. Leaf size=32 \[ \text {Int}\left (\frac {\sqrt {a+b x+c x^2} (d+e x)^m}{f+g x},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.03, 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 = {} \[ \int \frac {(d+e x)^m \sqrt {a+b x+c x^2}}{f+g x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {(d+e x)^m \sqrt {a+b x+c x^2}}{f+g x} \, dx &=\int \frac {(d+e x)^m \sqrt {a+b x+c x^2}}{f+g x} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.11, size = 0, normalized size = 0.00 \[ \int \frac {(d+e x)^m \sqrt {a+b x+c x^2}}{f+g x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.38, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sqrt {c x^{2} + b x + a} {\left (e x + d\right )}^{m}}{g x + f}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {c x^{2} + b x + a} {\left (e x + d\right )}^{m}}{g x + f}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.13, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {c \,x^{2}+b x +a}\, \left (e x +d \right )^{m}}{g x +f}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {c x^{2} + b x + a} {\left (e x + d\right )}^{m}}{g x + f}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {{\left (d+e\,x\right )}^m\,\sqrt {c\,x^2+b\,x+a}}{f+g\,x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (d + e x\right )^{m} \sqrt {a + b x + c x^{2}}}{f + g x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________