The integral ∫3xdx/√(1-2x) can be solved using the substitution method. The correct substitution is u = 1 - 2x, which leads to du = -2dx. By expressing x in terms of u, specifically x = (1/2)(1 - u), the integral can be simplified effectively. This method eliminates the x variable under the square root, allowing for a straightforward integration process.
PREREQUISITESStudents studying calculus, particularly those focusing on integration techniques, as well as educators looking for examples of u-substitution in practice.
Your second substitution will work if you replace x and dx with the corresponding values of u and du. Note that if u = 1 - 2x, then x = (1/2)(1 - u).zachem62 said:Homework Statement
∫3xdx/√(1-2x)
Homework Equations
The Attempt at a Solution
so i tried making u=3x which makes du=3dx but that substitution doesn't get rid of the x unde the square root. i tried u=1-2x and that gives du=-2dx and that doesn't get rid of the x on top. So I'm stuck and have no idea what to do here. Please help me out. Thanks!