Optimal. Leaf size=59 \[ 5 a^3 b^2 x^2+\frac{10}{3} a^2 b^3 x^3+5 a^4 b x+a^5 \log (x)+\frac{5}{4} a b^4 x^4+\frac{b^5 x^5}{5} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0175937, antiderivative size = 59, normalized size of antiderivative = 1., 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} \[ 5 a^3 b^2 x^2+\frac{10}{3} a^2 b^3 x^3+5 a^4 b x+a^5 \log (x)+\frac{5}{4} a b^4 x^4+\frac{b^5 x^5}{5} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^5}{x} \, dx &=\int \left (5 a^4 b+\frac{a^5}{x}+10 a^3 b^2 x+10 a^2 b^3 x^2+5 a b^4 x^3+b^5 x^4\right ) \, dx\\ &=5 a^4 b x+5 a^3 b^2 x^2+\frac{10}{3} a^2 b^3 x^3+\frac{5}{4} a b^4 x^4+\frac{b^5 x^5}{5}+a^5 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0048367, size = 59, normalized size = 1. \[ 5 a^3 b^2 x^2+\frac{10}{3} a^2 b^3 x^3+5 a^4 b x+a^5 \log (x)+\frac{5}{4} a b^4 x^4+\frac{b^5 x^5}{5} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 54, normalized size = 0.9 \begin{align*} 5\,{a}^{4}bx+5\,{a}^{3}{b}^{2}{x}^{2}+{\frac{10\,{a}^{2}{b}^{3}{x}^{3}}{3}}+{\frac{5\,a{b}^{4}{x}^{4}}{4}}+{\frac{{b}^{5}{x}^{5}}{5}}+{a}^{5}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.05842, size = 72, normalized size = 1.22 \begin{align*} \frac{1}{5} \, b^{5} x^{5} + \frac{5}{4} \, a b^{4} x^{4} + \frac{10}{3} \, a^{2} b^{3} x^{3} + 5 \, a^{3} b^{2} x^{2} + 5 \, a^{4} b x + a^{5} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.58551, size = 120, normalized size = 2.03 \begin{align*} \frac{1}{5} \, b^{5} x^{5} + \frac{5}{4} \, a b^{4} x^{4} + \frac{10}{3} \, a^{2} b^{3} x^{3} + 5 \, a^{3} b^{2} x^{2} + 5 \, a^{4} b x + a^{5} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.360342, size = 60, normalized size = 1.02 \begin{align*} a^{5} \log{\left (x \right )} + 5 a^{4} b x + 5 a^{3} b^{2} x^{2} + \frac{10 a^{2} b^{3} x^{3}}{3} + \frac{5 a b^{4} x^{4}}{4} + \frac{b^{5} x^{5}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.19554, size = 73, normalized size = 1.24 \begin{align*} \frac{1}{5} \, b^{5} x^{5} + \frac{5}{4} \, a b^{4} x^{4} + \frac{10}{3} \, a^{2} b^{3} x^{3} + 5 \, a^{3} b^{2} x^{2} + 5 \, a^{4} b x + a^{5} \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]