Learn how to solve problems step by step online. Integrate the function 1/(x^(-3)(1+x^2)^(1/2)) from 1 to infinity. Since the exponent of the denominator is negative, we can bring it to the numerator and thus simplify. We can solve the integral \int\frac{x^{3}}{\sqrt{1+x^2}}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above. Substituting in the original integral, we get.

Integrate the function 1/(x^(-3)(1+x^2)^(1/2)) from 1 to infinity