Optimal. Leaf size=15 \[ \frac{\log \left (a+b x^n\right )}{b n} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0050448, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {260} \[ \frac{\log \left (a+b x^n\right )}{b n} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 260
Rubi steps
\begin{align*} \int \frac{x^{-1+n}}{a+b x^n} \, dx &=\frac{\log \left (a+b x^n\right )}{b n}\\ \end{align*}
Mathematica [A] time = 0.0013722, size = 15, normalized size = 1. \[ \frac{\log \left (a+b x^n\right )}{b n} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 18, normalized size = 1.2 \begin{align*}{\frac{\ln \left ( a+b{{\rm e}^{n\ln \left ( x \right ) }} \right ) }{bn}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.96682, size = 20, normalized size = 1.33 \begin{align*} \frac{\log \left (b x^{n} + a\right )}{b n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0.997572, size = 30, normalized size = 2. \begin{align*} \frac{\log \left (b x^{n} + a\right )}{b n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 3.16469, size = 27, normalized size = 1.8 \begin{align*} \begin{cases} \frac{\log{\left (x \right )}}{a} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left (x \right )}}{a + b} & \text{for}\: n = 0 \\\frac{x^{n}}{a n} & \text{for}\: b = 0 \\\frac{\log{\left (\frac{a}{b} + x^{n} \right )}}{b n} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.1221, size = 22, normalized size = 1.47 \begin{align*} \frac{\log \left ({\left | b x^{n} + a \right |}\right )}{b n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]