Optimal. Leaf size=20 \[ -\frac {a^2}{x}+2 a b \log (x)+b^2 x \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {43} \[ -\frac {a^2}{x}+2 a b \log (x)+b^2 x \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^2}{x^2} \, dx &=\int \left (b^2+\frac {a^2}{x^2}+\frac {2 a b}{x}\right ) \, dx\\ &=-\frac {a^2}{x}+b^2 x+2 a b \log (x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 20, normalized size = 1.00 \[ -\frac {a^2}{x}+2 a b \log (x)+b^2 x \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.41, size = 24, normalized size = 1.20 \[ \frac {b^{2} x^{2} + 2 \, a b x \log \relax (x) - a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.09, size = 21, normalized size = 1.05 \[ b^{2} x + 2 \, a b \log \left ({\left | x \right |}\right ) - \frac {a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 21, normalized size = 1.05 \[ 2 a b \ln \relax (x )+b^{2} x -\frac {a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.10, size = 20, normalized size = 1.00 \[ b^{2} x + 2 \, a b \log \relax (x) - \frac {a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.07, size = 20, normalized size = 1.00 \[ b^2\,x-\frac {a^2}{x}+2\,a\,b\,\ln \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.13, size = 17, normalized size = 0.85 \[ - \frac {a^{2}}{x} + 2 a b \log {\relax (x )} + b^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________