\int (dx)/((a^(2)+x^(2)+b^(2))^((3)/(2)))
You asked:
Evaluate the integral: \(\int{\frac{1}{{\left( {a}^{2} + {x}^{2} + {b}^{2} \right)}^{\frac{3}{2}}}}dx\)
MathBot Answer:
Antiderivative
\[\int{\frac{1}{{\left( {a}^{2} + {x}^{2} + {b}^{2} \right)}^{\frac{3}{2}}}}dx = \frac{x}{\sqrt{1 + \frac{x^{2}}{\operatorname{polar\_lift}{\left(a^{2} + b^{2} \right)}}} \operatorname{polar\_lift}^{\frac{3}{2}}{\left(a^{2} + b^{2} \right)}} + C\]