Optimal. Leaf size=53 \[ \frac{a^2 x^5}{5 b^3}-\frac{a^3 \log \left (a+b x^5\right )}{5 b^4}-\frac{a x^{10}}{10 b^2}+\frac{x^{15}}{15 b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.034639, antiderivative size = 53, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac{a^2 x^5}{5 b^3}-\frac{a^3 \log \left (a+b x^5\right )}{5 b^4}-\frac{a x^{10}}{10 b^2}+\frac{x^{15}}{15 b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^{19}}{a+b x^5} \, dx &=\frac{1}{5} \operatorname{Subst}\left (\int \frac{x^3}{a+b x} \, dx,x,x^5\right )\\ &=\frac{1}{5} \operatorname{Subst}\left (\int \left (\frac{a^2}{b^3}-\frac{a x}{b^2}+\frac{x^2}{b}-\frac{a^3}{b^3 (a+b x)}\right ) \, dx,x,x^5\right )\\ &=\frac{a^2 x^5}{5 b^3}-\frac{a x^{10}}{10 b^2}+\frac{x^{15}}{15 b}-\frac{a^3 \log \left (a+b x^5\right )}{5 b^4}\\ \end{align*}
Mathematica [A] time = 0.0052603, size = 53, normalized size = 1. \[ \frac{a^2 x^5}{5 b^3}-\frac{a^3 \log \left (a+b x^5\right )}{5 b^4}-\frac{a x^{10}}{10 b^2}+\frac{x^{15}}{15 b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 46, normalized size = 0.9 \begin{align*}{\frac{{x}^{5}{a}^{2}}{5\,{b}^{3}}}-{\frac{a{x}^{10}}{10\,{b}^{2}}}+{\frac{{x}^{15}}{15\,b}}-{\frac{{a}^{3}\ln \left ( b{x}^{5}+a \right ) }{5\,{b}^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.86538, size = 62, normalized size = 1.17 \begin{align*} -\frac{a^{3} \log \left (b x^{5} + a\right )}{5 \, b^{4}} + \frac{2 \, b^{2} x^{15} - 3 \, a b x^{10} + 6 \, a^{2} x^{5}}{30 \, b^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.71543, size = 101, normalized size = 1.91 \begin{align*} \frac{2 \, b^{3} x^{15} - 3 \, a b^{2} x^{10} + 6 \, a^{2} b x^{5} - 6 \, a^{3} \log \left (b x^{5} + a\right )}{30 \, b^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.510664, size = 44, normalized size = 0.83 \begin{align*} - \frac{a^{3} \log{\left (a + b x^{5} \right )}}{5 b^{4}} + \frac{a^{2} x^{5}}{5 b^{3}} - \frac{a x^{10}}{10 b^{2}} + \frac{x^{15}}{15 b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.16539, size = 63, normalized size = 1.19 \begin{align*} -\frac{a^{3} \log \left ({\left | b x^{5} + a \right |}\right )}{5 \, b^{4}} + \frac{2 \, b^{2} x^{15} - 3 \, a b x^{10} + 6 \, a^{2} x^{5}}{30 \, b^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]