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Title: Integrations of the simplest irrational functions
Description: Comprehensive notes and practicals (Problems and Solutions) covering: -Integrations of the simplest irrational functions
Description: Comprehensive notes and practicals (Problems and Solutions) covering: -Integrations of the simplest irrational functions
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An irrational function is a
function that has an
argument over which the
root is extracted
...
Therefore, we consider
only the simplest types of
integrals
...
ax b
ax
b
x,
R
,
...
m/n
r/s
For the calculation of
integrals of this type,
substitution is recommended:
ax b k
t ,
cx d
where k – lowest common
multiple of denominators
of fractions:
m
r
,
...
Therefore, such a
substitution is called
rationalizing
...
Find the integral:
I
dx
3
( 2x 1) 2x 1
2
Answer:
...
6
1
...
4
x x
xt
...
To find integrals of this
type, it is recommended:
- selection under the root of
the full square;
- substitution:
b
x t
...
1
...
Answer:
t
I 7 t 3 arcsin C
...
2
Title: Integrations of the simplest irrational functions
Description: Comprehensive notes and practicals (Problems and Solutions) covering: -Integrations of the simplest irrational functions
Description: Comprehensive notes and practicals (Problems and Solutions) covering: -Integrations of the simplest irrational functions