
When to do u-substitution and when to integrate by parts
A good rule of thumb to follow would be to try u-substitution first, and then if you cannot reformulate your function into the correct form, try integration by parts.
calculus - How do I pick the right "u" for u substitution and when do I ...
Jan 24, 2021 · u u -sub is basically anti-chain rule. If you can do lots of chain rule differentiations in your head, you will be able to spot the analogous u u -sub when it arises. For example, if you can easily …
Integration by parts vs u-substitution - Mathematics Stack Exchange
Nov 14, 2018 · In calculus we progressively learned definite integrals, indefinite integrals, u-substitution of integrals, and now integration by parts. So the confusion lies here.
calculus - U-sub without changing the bounds of integration ...
Apr 11, 2021 · The best way to do that is to use a substitution, namely you will let u = sin(x) du = cos(x)dx u = sin (x) d u = cos (x) d x, And you have to change the bounds of integration, so the …
Integration by substitution, why do we change the limits?
The underlying reason is that integration comes from Riemann sums, the function values depend on the interval of integration. When you change the interval, the heights of the rectangles you use in the …
Integration by parts using u-substitution and square root
I have to use the technique of integration by parts to evaluate the integrals. I'm having trouble with a particular problem: $$ \\int x (\\sqrt{x+2}) dx $$ I'm using u-substitution, but since I'm a...
calculus - Integration by Parts implies U-substitution? - Mathematics ...
One can check that if you start with some integral, which can be see as an "obvious u-substitution problem", that you can instead use integration by parts, and wind up with the scenario where you …
calculus - Why is it that, when using the u-substitution rule, you ...
Dec 4, 2018 · You can do the substitution in an indefinite integral, and then use the answer you get there to find the definite one. That requires: (i) doing the indefinite integral separately, because it is not the …
How to choose U in U-substitution integration method.
Sep 13, 2020 · Sometimes U-Sub doesn't work with quotients, you will need to solve by partial fraction decomposition method, why doesn't U-Sub work in this case? Can someone explain why? Sorry if I …
calculus - How can we visualise integration by substitution ...
Nov 25, 2018 · When we use u-substitution, we replace dx with du. But clearly du is not constant as it changes with x. To me, this doesn't make sense because how do we integrate with respect to …