Exercise
$\int_0^{3a}\left(\frac{2x}{\left(x^2-a^2\right)^{\frac{2}{3}}}\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Integrate the function (2x)/((x^2-a^2)^(2/3)) from 0 to 3a. Take out the constant 2 from the integral. We can solve the integral 2\int\frac{x}{\sqrt[3]{\left(x^2-a^2\right)^{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 (2x)/((x^2-a^2)^(2/3)) from 0 to 3a
Final answer to the exercise
$3\left(\frac{\sqrt[3]{\left(3a\right)^2-a^2}}{\sqrt[3]{a^{2}}}\right)\sqrt[3]{a^{2}}- 3\left(\frac{\sqrt[3]{0^2-a^2}}{\sqrt[3]{a^{2}}}\right)\sqrt[3]{a^{2}}$