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Title: Integration by parts (Mathematics)
Description: Comprehensive notes and practicals (Problems and Solutions) covering: -Integration by parts
Description: Comprehensive notes and practicals (Problems and Solutions) covering: -Integration by parts
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Suppose there are two
differentiable functions:
u u(x) and v v(x)
...
Integrating, we get the
integration formula by parts:
udv
uv
vdu
...
The following types of
integrals are found by the
method of integration by
parts:
1
...
kx
2
...
b) P(x) cos(kx)dx
...
When calculating these
integrals by parts, for u it is
necessary to take P (x)
...
P( x)
dx
...
P( x)
dx
...
P(x) ln(kx)dx
...
sin(kx)
6
...
cos(kx)
ax
When calculating these
integrals in parts, for u should
be taken
ax
e
...
Find the integral:
I e xdx
x
Answer:
I xe e C
x
x
2
...
Find the integral:
I e cos xdx
x
Answer:
1 x
I e (sin x cos x) C
2
4
Title: Integration by parts (Mathematics)
Description: Comprehensive notes and practicals (Problems and Solutions) covering: -Integration by parts
Description: Comprehensive notes and practicals (Problems and Solutions) covering: -Integration by parts