Exercise
$\int_{1}^{\infty}\frac{7}{\sqrt[7]{x}}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Integrate the function 7/(x^(1/7)) from 1 to infinity. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. Multiply the fraction and term in - \frac{1}{7}. The integral of a function times a constant (7) is equal to the constant times the integral of the function. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as -\frac{1}{7}.
Integrate the function 7/(x^(1/7)) from 1 to infinity
Final answer to the exercise
The integral diverges.