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!
The purpose of "U substitution" is to simplify integrals by replacing a complex expression with a simpler one. It allows us to solve integrals that may not be possible to solve using other integration techniques.
You should use "U substitution" when the integral contains a function and its derivative, or when the integral contains a polynomial expression within a square root. It can also be used when the integral contains a product of trigonometric functions.
The steps for solving a "U substitution" problem are: 1. Identify the function to be substituted (usually the inner function of a composite function).2. Let u be equal to this function.3. Calculate du, the derivative of u, with respect to the variable of integration.4. Rewrite the integral in terms of u and du.5. Integrate the new simplified integral.6. Substitute back u with the original function to get the final answer.
Yes, "U substitution" can be used for both indefinite and definite integrals. When solving a definite integral, you will need to substitute the limits of integration as well.
Yes, there are some limitations to using "U substitution". It cannot be used for integrals containing exponential or logarithmic functions. It also may not work for all integrals, and in some cases, other integration techniques may be more suitable.