Optimal. Leaf size=12 \[ -\frac{1}{d (c+d x)} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0016551, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {32} \[ -\frac{1}{d (c+d x)} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 32
Rubi steps
\begin{align*} \int \frac{1}{(c+d x)^2} \, dx &=-\frac{1}{d (c+d x)}\\ \end{align*}
Mathematica [A] time = 0.0023961, size = 12, normalized size = 1. \[ -\frac{1}{d (c+d x)} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 13, normalized size = 1.1 \begin{align*} -{\frac{1}{d \left ( dx+c \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.961277, size = 16, normalized size = 1.33 \begin{align*} -\frac{1}{{\left (d x + c\right )} d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.56419, size = 24, normalized size = 2. \begin{align*} -\frac{1}{d^{2} x + c d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.291893, size = 10, normalized size = 0.83 \begin{align*} - \frac{1}{c d + d^{2} x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.08254, size = 16, normalized size = 1.33 \begin{align*} -\frac{1}{{\left (d x + c\right )} d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]