Integration by parts is for functions that can be written as the product of another function and a third function's derivative. $$\int u dv$$ A good rule of thumb to follow would be to try u-substitution first, …

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 …

Jul 16, 2014 · I've highlighted the part I don't understand in red. Why do we change the limits of integration here? What difference does it make? Source of Quotation: Calculus: Early …

Apr 11, 2021 · So there really is a difference in the way people write vs how they think, especially in publications like textbooks with high editorial standards. You should continue to think however you …

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.

May 26, 2018 · How do I know whether to try a u-substitution or integration by parts first when there isn't an apparent function I can differentiate and easily replace within the integral?

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 …

You should use hyperbolic substitution in functions like $\frac {1} {\sqrt {x^2-1}}$. Substitute $x=\cosh (u)$, and from here on out just work out the integral like normal.

Dec 9, 2011 · 8 First of all I would like to start off by asking why do they have different change of variable formulas for definite integrals than indefinite...why cant we just integrate using U substitution …

To be precise all of that falls under general substitution where u-substitution and trig substitution are special cases