Optimal. Leaf size=35 \[ \text {Int}\left (\frac {(a g+b g x)^2}{B \log \left (\frac {e (c+d x)}{a+b x}\right )+A},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.20, 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 = {} \[ \int \frac {(a g+b g x)^2}{A+B \log \left (\frac {e (c+d x)}{a+b x}\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {(a g+b g x)^2}{A+B \log \left (\frac {e (c+d x)}{a+b x}\right )} \, dx &=\int \left (\frac {a^2 g^2}{A+B \log \left (\frac {e (c+d x)}{a+b x}\right )}+\frac {2 a b g^2 x}{A+B \log \left (\frac {e (c+d x)}{a+b x}\right )}+\frac {b^2 g^2 x^2}{A+B \log \left (\frac {e (c+d x)}{a+b x}\right )}\right ) \, dx\\ &=\left (a^2 g^2\right ) \int \frac {1}{A+B \log \left (\frac {e (c+d x)}{a+b x}\right )} \, dx+\left (2 a b g^2\right ) \int \frac {x}{A+B \log \left (\frac {e (c+d x)}{a+b x}\right )} \, dx+\left (b^2 g^2\right ) \int \frac {x^2}{A+B \log \left (\frac {e (c+d x)}{a+b x}\right )} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.60, size = 0, normalized size = 0.00 \[ \int \frac {(a g+b g x)^2}{A+B \log \left (\frac {e (c+d x)}{a+b x}\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.76, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {b^{2} g^{2} x^{2} + 2 \, a b g^{2} x + a^{2} g^{2}}{B \log \left (\frac {d e x + c e}{b x + a}\right ) + A}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [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]
[Out]
________________________________________________________________________________________
maple [A] time = 1.17, size = 0, normalized size = 0.00 \[ \int \frac {\left (b g x +a g \right )^{2}}{B \ln \left (\frac {\left (d x +c \right ) e}{b x +a}\right )+A}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b g x + a g\right )}^{2}}{B \log \left (\frac {{\left (d x + c\right )} e}{b x + a}\right ) + A}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {{\left (a\,g+b\,g\,x\right )}^2}{A+B\,\ln \left (\frac {e\,\left (c+d\,x\right )}{a+b\,x}\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ g^{2} \left (\int \frac {a^{2}}{A + B \log {\left (\frac {c e}{a + b x} + \frac {d e x}{a + b x} \right )}}\, dx + \int \frac {b^{2} x^{2}}{A + B \log {\left (\frac {c e}{a + b x} + \frac {d e x}{a + b x} \right )}}\, dx + \int \frac {2 a b x}{A + B \log {\left (\frac {c e}{a + b x} + \frac {d e x}{a + b x} \right )}}\, dx\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________