Question

How to integrate by parts ​

Answer 1

Answer:

just read it and follow the steps according to ILATE

Answer 2

Answer:

$\large\boxed{\sf{\displaystyle \int uv \: dx = u\displaystyle \int v \: dx - \displaystyle \int( \frac{d}{dx} u \int v \: dx)dx}}$

Step-by-step explanation:

Let u and v be two differentiable functions of a single variable x.

Then tge integral of the product of the two functions is given by:

$\purple{\displaystyle \int uv \: dx = u\displaystyle \int v \: dx - \displaystyle \int( \frac{d}{dx} u \int v \: dx)dx}$

If two functions are of two different types, then consider the first function (i.e. u) which comes first in word ILATE where

I : inverse trignometric function

L : logarithmic function

A : algebraic function

T : trignometric function

E : exponential function