# Improper Integral – A functions multiplication with roots on an infinite interval – Exercise 6991

Exercise

Evaluate the integral

$$\int_{1}^{\infty} (\frac{1}{x^3}-\frac{1}{x^4})\sqrt{x\sqrt{x}} dx$$

$$\int_{1}^{\infty} (\frac{1}{x^3}-\frac{1}{x^4})\sqrt{x\sqrt{x}} dx=\frac{16}{45}$$