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$\int_{\frac{\sqrt{6}}{3}}^{\frac{2}{3}}\frac{1}{x^5\sqrt{9x^2-1}}dx$
Learn how to solve problems step by step online. Integrate the function 1/(x^5(9x^2-1)^1/2) from 2/3^1/2 to 2/3. Simplifying. Since the upper limit of the integral is less than the lower one, we can rewrite the limits by applying the inverse property of integration limits: If we invert the limits of an integral, it changes sign: \int_a^bf(x)dx=-\int_b^af(x)dx. First, factor the terms inside the radical by 9 for an easier handling. Taking the constant out of the radical.