Optimal. Leaf size=25 \[ \frac{x^{10}}{10}-\frac{x^5}{5}+\frac{1}{5} \log \left (x^5+1\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0118298, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {266, 43} \[ \frac{x^{10}}{10}-\frac{x^5}{5}+\frac{1}{5} \log \left (x^5+1\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^{14}}{1+x^5} \, dx &=\frac{1}{5} \operatorname{Subst}\left (\int \frac{x^2}{1+x} \, dx,x,x^5\right )\\ &=\frac{1}{5} \operatorname{Subst}\left (\int \left (-1+x+\frac{1}{1+x}\right ) \, dx,x,x^5\right )\\ &=-\frac{x^5}{5}+\frac{x^{10}}{10}+\frac{1}{5} \log \left (1+x^5\right )\\ \end{align*}
Mathematica [A] time = 0.0045356, size = 22, normalized size = 0.88 \[ \frac{1}{10} \left (x^{10}-2 x^5+2 \log \left (x^5+1\right )-3\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 20, normalized size = 0.8 \begin{align*} -{\frac{{x}^{5}}{5}}+{\frac{{x}^{10}}{10}}+{\frac{\ln \left ({x}^{5}+1 \right ) }{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.983718, size = 26, normalized size = 1.04 \begin{align*} \frac{1}{10} \, x^{10} - \frac{1}{5} \, x^{5} + \frac{1}{5} \, \log \left (x^{5} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.7088, size = 54, normalized size = 2.16 \begin{align*} \frac{1}{10} \, x^{10} - \frac{1}{5} \, x^{5} + \frac{1}{5} \, \log \left (x^{5} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.103791, size = 17, normalized size = 0.68 \begin{align*} \frac{x^{10}}{10} - \frac{x^{5}}{5} + \frac{\log{\left (x^{5} + 1 \right )}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.22031, size = 27, normalized size = 1.08 \begin{align*} \frac{1}{10} \, x^{10} - \frac{1}{5} \, x^{5} + \frac{1}{5} \, \log \left ({\left | x^{5} + 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]