Optimal. Leaf size=12 \[ \frac{1}{b (a-b x)} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0061974, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {627, 32} \[ \frac{1}{b (a-b x)} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 627
Rule 32
Rubi steps
\begin{align*} \int \frac{(a+b x)^2}{\left (a^2-b^2 x^2\right )^2} \, dx &=\int \frac{1}{(a-b x)^2} \, dx\\ &=\frac{1}{b (a-b x)}\\ \end{align*}
Mathematica [A] time = 0.0020324, size = 12, normalized size = 1. \[ \frac{1}{b (a-b x)} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.037, size = 15, normalized size = 1.3 \begin{align*} -{\frac{1}{b \left ( bx-a \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.32449, size = 19, normalized size = 1.58 \begin{align*} -\frac{1}{b^{2} x - a b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.70612, size = 24, normalized size = 2. \begin{align*} -\frac{1}{b^{2} x - a b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.296404, size = 10, normalized size = 0.83 \begin{align*} - \frac{1}{- a b + b^{2} x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.19993, size = 19, normalized size = 1.58 \begin{align*} -\frac{1}{{\left (b x - a\right )} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]