** Final Answer

**

** Step-by-step Solution **

Problem to solve:

** Specify the solving method

**

**

The integral of a function times a constant ($8$) is equal to the constant times the integral of the function

Learn how to solve integral calculus problems step by step online.

$8\int x^2\cos\left(x^3\right)dx$

Learn how to solve integral calculus problems step by step online. Find the integral int(8x^2cos(x^3))dx. The integral of a function times a constant (8) is equal to the constant times the integral of the function. We can solve the integral \int x^2\cos\left(x^3\right)dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that x^3 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dx in the previous equation.

** Final Answer

**