What is you Integration?

Answer 1

I think you mean "u" substitution in integration.

If an integral is too complicated to be solved using simple integration, part of the integral can be substituted for "u".

Here is an example:

∫8x(4x²+7)³dx

To solve this, you need a u substitution.

Let's let u=4x²+7

Now, we can't still have x's in the equation if there is the new variable of u, so we need to change dx into du. To do this, we differentiate u.

du=8xdx

Luckily, we have that 8x in the integral already.

After substituting the new u substitution in, the integral reads:

∫u³du

Now, all we need to do is integrate!

Once we integrate, we come up with u⁴/4 + C

However, we have to bring it back into terms of x. If you recall u=4x²+7, so let's back-substitute.

y = (4x²+7)⁴/4 + C

And there you go! A successful u substitution!