Exam Question: Integration using a u-substitution

Integration using u-Substitution
With all u-substitution integration problems:
The FIRST STEP is to pick your "u". The best choice is usually the longer x-expression that is inside a power or a square root or the denominator, etc (in an "inside function"). Set u equal to this x-expression.
The SECOND STEP is to find "du" by taking the derivative of the u expression with respect to x. For instance, if you have u=3x+2, your du would then be du=3dx. **NOTE: Remember to include "dx" at the end of your du differential expression.
The THIRD STEP is to substitute u and du into the integral everywhere in place of x and dx. **NOTE: if your du does not perfectly match what you need in order to completely substitute before integrating, you must rearrange the du, or sometimes rearrange the u, in order to fully substitute before integrating.
The FOURTH STEP is to integrate, remembering to add "+ C" at the end since you integrated an indefinite integral (no limits). The du goes away when you integrate.
The LAST STEP is to "back-substitute" by replacing everywhere u appear with the x-expression that you chose u to be.
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[@omnamahshivaya458]

You are doing God's work Harold, bless you!

[@HaroldWalden]

Thanks for the nice words, I really appreciate it.

[@silentintegrals9104]

totally agree, awesome ... stay curious

[@silentintegrals9104]

💕💕💕 awesome, solving integrals is so much fun 💕💕💕

[@HaroldWalden]

It really is!