Question

what is by part intrigration.....give an example...​

Answer 1

$\boxed{ \bold{ \red{part \: intrigration}}}$

Integration by parts is a technique for performing indefinite integration or definite integration by expanding the differential of a product of functions and expressing the original integral in terms of a known integral .

$\boxed{ \bold{ \red{example}}}$

What is ∫x cos(x) dx ? OK, we have x multiplied by cos(x), so integration by parts is a good choice. First choose which functions for u and v: u = x.

Answer 2

Answer:

Integration by Parts

Integration by Parts is a special method of integration that is often useful when two functions are multiplied together, but is also helpful in other ways.

You will see plenty of examples soon, but first let us see the rule:

∫u v dx = u∫v dx −∫u' (∫v dx) dx

u is the function u(x)

v is the function v(x)

u' is the derivative of the function u(x)

Step-by-step explanation:

we followed these steps:

Choose u and v

Differentiate u: u'

Integrate v: ∫v dx

Put u, u' and ∫v dx into: u∫v dx −∫u' (∫v dx) dx

Simplify and solve

In English, to help you remember, ∫u v dx becomes:

(u integral v) minus integral of (derivative u, integral v)

Let's try some more examples:

Example: What is ∫ln(x)/x2 dx ?

First choose u and v:

u = ln(x)

v = 1/x2