## How do you calculate U in substitution?

u is just the variable that was chosen to represent what you replace. du and dx are just parts of a derivative, where of course u is substituted part fo the function. u will always be some function of x, so you take the derivative of u with respect to x, or in other words du/dx.

## When should I use U substitution?

You use the U-substitution whenever you find that your integrand can be factored out into two separate functions, one of which is the derivative function of the other. If you see this attribute in your integrand, then the U-substitution can be effectively used.

**How do you use substitution rule in integration?**

Integration by Substitution

- Note that we have g(x) and its derivative g'(x) Like in this example:
- Here f=cos, and we have g=x2 and its derivative 2x. This integral is good to go!
- Then we can integrate f(u), and finish by putting g(x) back as u. Like this:

**Why do we use integration by substitution?**

Usually the method of integration by substitution is extremely useful when we make a substitution for a function whose derivative is also present in the integrand. Doing so, the function simplifies and then the basic formulas of integration can be used to integrate the function.

### Why does substitution work in integration?

We substitute an algebraic function by a trigonometric function because a trigonometric substitution helps us to get a perfect square under the radical sign. This simplifies the integrand function. and thus we can do standard substitution, as it helps to get a perfect square.

### What is the rule of substitution?

The substitution rule is a trick for evaluating integrals. It is based on the following identity between differentials (where u is a function of x): du = u dx . 1 + x2 2x dx.

**Does substitution always work?**

Always do a u-sub if you can; if you cannot, consider integration by parts. A u-sub can be done whenever you have something containing a function (we’ll call this g), and that something is multiplied by the derivative of g. That is, if you have ∫f(g(x))g′(x)dx, use a u-sub.