Exercise
$\int24x\left(6-x^2\right)^{\frac{1}{3}}dx$
Step-by-step Solution
Learn how to solve differential calculus problems step by step online. Integrate int(24x(6-x^2)^(1/3))dx. The integral of a function times a constant (24) is equal to the constant times the integral of the function. We can solve the integral 24\int x\sqrt[3]{6-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 int(24x(6-x^2)^(1/3))dx
Final answer to the exercise
$\frac{-54\sqrt[3]{6}\sqrt[3]{\left(6-x^2\right)^{4}}}{\sqrt[3]{\left(6\right)^{4}}}+C_0$