Optimal. Leaf size=60 \[ -\frac{10 a^3 b^2}{x}+10 a^2 b^3 \log (x)-\frac{5 a^4 b}{2 x^2}-\frac{a^5}{3 x^3}+5 a b^4 x+\frac{b^5 x^2}{2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0216694, antiderivative size = 60, 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} \[ -\frac{10 a^3 b^2}{x}+10 a^2 b^3 \log (x)-\frac{5 a^4 b}{2 x^2}-\frac{a^5}{3 x^3}+5 a b^4 x+\frac{b^5 x^2}{2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^5}{x^4} \, dx &=\int \left (5 a b^4+\frac{a^5}{x^4}+\frac{5 a^4 b}{x^3}+\frac{10 a^3 b^2}{x^2}+\frac{10 a^2 b^3}{x}+b^5 x\right ) \, dx\\ &=-\frac{a^5}{3 x^3}-\frac{5 a^4 b}{2 x^2}-\frac{10 a^3 b^2}{x}+5 a b^4 x+\frac{b^5 x^2}{2}+10 a^2 b^3 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0058558, size = 60, normalized size = 1. \[ -\frac{10 a^3 b^2}{x}+10 a^2 b^3 \log (x)-\frac{5 a^4 b}{2 x^2}-\frac{a^5}{3 x^3}+5 a b^4 x+\frac{b^5 x^2}{2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.005, size = 55, normalized size = 0.9 \begin{align*} -{\frac{{a}^{5}}{3\,{x}^{3}}}-{\frac{5\,{a}^{4}b}{2\,{x}^{2}}}-10\,{\frac{{a}^{3}{b}^{2}}{x}}+5\,a{b}^{4}x+{\frac{{b}^{5}{x}^{2}}{2}}+10\,{a}^{2}{b}^{3}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.02227, size = 74, normalized size = 1.23 \begin{align*} \frac{1}{2} \, b^{5} x^{2} + 5 \, a b^{4} x + 10 \, a^{2} b^{3} \log \left (x\right ) - \frac{60 \, a^{3} b^{2} x^{2} + 15 \, a^{4} b x + 2 \, a^{5}}{6 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.48722, size = 132, normalized size = 2.2 \begin{align*} \frac{3 \, b^{5} x^{5} + 30 \, a b^{4} x^{4} + 60 \, a^{2} b^{3} x^{3} \log \left (x\right ) - 60 \, a^{3} b^{2} x^{2} - 15 \, a^{4} b x - 2 \, a^{5}}{6 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.481205, size = 58, normalized size = 0.97 \begin{align*} 10 a^{2} b^{3} \log{\left (x \right )} + 5 a b^{4} x + \frac{b^{5} x^{2}}{2} - \frac{2 a^{5} + 15 a^{4} b x + 60 a^{3} b^{2} x^{2}}{6 x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.2318, size = 76, normalized size = 1.27 \begin{align*} \frac{1}{2} \, b^{5} x^{2} + 5 \, a b^{4} x + 10 \, a^{2} b^{3} \log \left ({\left | x \right |}\right ) - \frac{60 \, a^{3} b^{2} x^{2} + 15 \, a^{4} b x + 2 \, a^{5}}{6 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]