Optimal. Leaf size=36 \[ -\frac{3 x^5}{5 b^2}+\frac{9 \log \left (b x^5+3\right )}{5 b^3}+\frac{x^{10}}{10 b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0245118, antiderivative size = 36, 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} \[ -\frac{3 x^5}{5 b^2}+\frac{9 \log \left (b x^5+3\right )}{5 b^3}+\frac{x^{10}}{10 b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^{14}}{3+b x^5} \, dx &=\frac{1}{5} \operatorname{Subst}\left (\int \frac{x^2}{3+b x} \, dx,x,x^5\right )\\ &=\frac{1}{5} \operatorname{Subst}\left (\int \left (-\frac{3}{b^2}+\frac{x}{b}+\frac{9}{b^2 (3+b x)}\right ) \, dx,x,x^5\right )\\ &=-\frac{3 x^5}{5 b^2}+\frac{x^{10}}{10 b}+\frac{9 \log \left (3+b x^5\right )}{5 b^3}\\ \end{align*}
Mathematica [A] time = 0.005524, size = 36, normalized size = 1. \[ -\frac{3 x^5}{5 b^2}+\frac{9 \log \left (b x^5+3\right )}{5 b^3}+\frac{x^{10}}{10 b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 31, normalized size = 0.9 \begin{align*} -{\frac{3\,{x}^{5}}{5\,{b}^{2}}}+{\frac{{x}^{10}}{10\,b}}+{\frac{9\,\ln \left ( b{x}^{5}+3 \right ) }{5\,{b}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.00468, size = 41, normalized size = 1.14 \begin{align*} \frac{b x^{10} - 6 \, x^{5}}{10 \, b^{2}} + \frac{9 \, \log \left (b x^{5} + 3\right )}{5 \, b^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.72883, size = 69, normalized size = 1.92 \begin{align*} \frac{b^{2} x^{10} - 6 \, b x^{5} + 18 \, \log \left (b x^{5} + 3\right )}{10 \, b^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.347588, size = 31, normalized size = 0.86 \begin{align*} \frac{x^{10}}{10 b} - \frac{3 x^{5}}{5 b^{2}} + \frac{9 \log{\left (b x^{5} + 3 \right )}}{5 b^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.37874, size = 42, normalized size = 1.17 \begin{align*} \frac{b x^{10} - 6 \, x^{5}}{10 \, b^{2}} + \frac{9 \, \log \left ({\left | b x^{5} + 3 \right |}\right )}{5 \, b^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]