Optimal. Leaf size=27 \[ 2 \sqrt{x}+4 \sqrt [4]{x}+4 \log \left (1-\sqrt [4]{x}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0116985, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {1593, 266, 43} \[ 2 \sqrt{x}+4 \sqrt [4]{x}+4 \log \left (1-\sqrt [4]{x}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1593
Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{1}{-\sqrt [4]{x}+\sqrt{x}} \, dx &=\int \frac{1}{\left (-1+\sqrt [4]{x}\right ) \sqrt [4]{x}} \, dx\\ &=4 \operatorname{Subst}\left (\int \frac{x^2}{-1+x} \, dx,x,\sqrt [4]{x}\right )\\ &=4 \operatorname{Subst}\left (\int \left (1+\frac{1}{-1+x}+x\right ) \, dx,x,\sqrt [4]{x}\right )\\ &=4 \sqrt [4]{x}+2 \sqrt{x}+4 \log \left (1-\sqrt [4]{x}\right )\\ \end{align*}
Mathematica [A] time = 0.0100669, size = 27, normalized size = 1. \[ 2 \sqrt{x}+4 \sqrt [4]{x}+4 \log \left (1-\sqrt [4]{x}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.007, size = 20, normalized size = 0.7 \begin{align*} 2\,\sqrt{x}+4\,\sqrt [4]{x}+4\,\ln \left ( \sqrt [4]{x}-1 \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.31642, size = 26, normalized size = 0.96 \begin{align*} 2 \, \sqrt{x} + 4 \, x^{\frac{1}{4}} + 4 \, \log \left (x^{\frac{1}{4}} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.17699, size = 59, normalized size = 2.19 \begin{align*} 2 \, \sqrt{x} + 4 \, x^{\frac{1}{4}} + 4 \, \log \left (x^{\frac{1}{4}} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.212634, size = 22, normalized size = 0.81 \begin{align*} 4 \sqrt [4]{x} + 2 \sqrt{x} + 4 \log{\left (\sqrt [4]{x} - 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.13031, size = 27, normalized size = 1. \begin{align*} 2 \, \sqrt{x} + 4 \, x^{\frac{1}{4}} + 4 \, \log \left ({\left | x^{\frac{1}{4}} - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]