\[ \int \frac {1}{\sqrt {b x^{2/3}+a x}} \, dx \]
Optimal antiderivative \[ \frac {2 \sqrt {b \,x^{\frac {2}{3}}+a x}}{a}-\frac {4 b \sqrt {b \,x^{\frac {2}{3}}+a x}}{a^{2} x^{\frac {1}{3}}} \]
command
integrate(1/(b*x^(2/3)+a*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {{\left (50331648 \, b^{7} + 10485760 \, b^{6} + 49152 \, {\left (512 \, a^{3} - 3\right )} b^{4} - 983040 \, b^{5} + 256 \, {\left (24576 \, a^{3} + 53\right )} b^{3} + 11648 \, a^{3} - 96 \, {\left (2048 \, a^{3} + 1\right )} b^{2} - 3 \, {\left (155648 \, a^{3} + 3\right )} b\right )} x + 2 \, {\left ({\left (16777216 \, a b^{6} + 6291456 \, a b^{5} + 196608 \, a b^{4} - 262144 \, a^{4} - 114688 \, a b^{3} - 2304 \, a b^{2} + 864 \, a b - 27 \, a\right )} x - 2 \, {\left (16777216 \, b^{7} + 6291456 \, b^{6} + 196608 \, b^{5} - 114688 \, b^{4} - 2304 \, b^{3} - {\left (262144 \, a^{3} + 27\right )} b + 864 \, b^{2}\right )} x^{\frac {2}{3}}\right )} \sqrt {a x + b x^{\frac {2}{3}}}}{{\left (16777216 \, a^{2} b^{6} + 6291456 \, a^{2} b^{5} + 196608 \, a^{2} b^{4} - 262144 \, a^{5} - 114688 \, a^{2} b^{3} - 2304 \, a^{2} b^{2} + 864 \, a^{2} b - 27 \, a^{2}\right )} x} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ \text {Timed out} \]