Подскажите как брать интеграл

Monique230

подскажите как брать интеграл от следующей функции:(a+b*cos(x^0.5)/(a+h+b*cos(x^1.5

mong

по дэ чему ? по dcos ?
если по х, то не берётся в элементарных функциях.

Monique230

по dx.

pilaf4

а как берётся?

mong

численно :confused:

vvasilevskiy

Скобки одной не хватает

pilaf4

если брать mathematica, то получается вполне себе в элементарных функциях для некоторых a, b, h.

Vlad128

а как берётся?

> int( (sqrt(a+b*cos(x /sqrta+h+b*cos(x^3 x );
memory used=3.8MB, alloc=2.9MB, time=0.07
memory used=7.6MB, alloc=4.3MB, time=0.16
memory used=11.4MB, alloc=4.8MB, time=0.24
memory used=15.2MB, alloc=5.2MB, time=0.34
/ 2 / a + b cos(x) \1/2 1/2 / a + b cos(x) \1/2 1/2
- 2 |-2 h a |--------------------| %3 EllipticE(%1, %2) sin(x) + a |--------------------| %3 h EllipticE(%1, %2) b sin(x)
\ \(a + b) (1 + cos(x/ \(a + b) (1 + cos(x/

2 / a + b cos(x) \1/2 1/2 2 2 / a + b cos(x) \1/2 1/2
- b cos(x) a |--------------------| %3 EllipticE(%1, %2) sin(x) - b cos(x) a |--------------------| %3 EllipticE(%1, %2) sin(x)
\(a + b) (1 + cos(x/ \(a + b) (1 + cos(x/

3 / a + b cos(x) \1/2 1/2 2 / a + b cos(x) \1/2 1/2
- a |--------------------| %3 EllipticE(%1, %2) sin(x) - h cos(x) a |--------------------| %3 EllipticE(%1, %2) sin(x)
\(a + b) (1 + cos(x/ \(a + b) (1 + cos(x/

3 / a + b cos(x) \1/2 1/2 / a + b cos(x) \1/2 1/2 2
- a cos(x) |--------------------| %3 EllipticE(%1, %2) sin(x) + a |--------------------| %3 b EllipticE(%1, %2) sin(x)
\(a + b) (1 + cos(x/ \(a + b) (1 + cos(x/

3 / a + b cos(x) \1/2 1/2 / a + b cos(x) \1/2 1/2 2 2 / a - b\1/2
+ b cos(x) |--------------------| %3 EllipticE(%1, %2) sin(x) + a cos(x) |--------------------| %3 b EllipticE(%1, %2) sin(x) - h a |- -----|
\(a + b) (1 + cos(x/ \(a + b) (1 + cos(x/ \ a + b/

3 / a + b cos(x) \1/2 1/2 2 2 / a + b cos(x) \1/2 1/2
+ b |--------------------| %3 EllipticE(%1, %2) sin(x) cos(x) - 2 h cos(x) a |--------------------| %3 EllipticE(%1, %2) sin(x)
\(a + b) (1 + cos(x/ \(a + b) (1 + cos(x/

/ a + b cos(x) \1/2 1/2 2 / a + b cos(x) \1/2 1/2 2 2
+ h sin(x) |--------------------| %3 b EllipticE(%1, %2) + h sin(x) |--------------------| %3 b EllipticE(%1, %2) cos(x)
\(a + b) (1 + cos(x/ \(a + b) (1 + cos(x/

2 / a + b cos(x) \1/2 1/2 / a - b\1/2 / a + b cos(x) \1/2 1/2 2
+ h cos(x) |--------------------| %3 EllipticE(%1, %2) b sin(x) + b a |- -----| h - 2 cos(x) h sin(x) |--------------------| %3 b EllipticF(%1, %2)
\(a + b) (1 + cos(x/ \ a + b/ \(a + b) (1 + cos(x/

2 / a - b\1/2 2 / a - b\1/2 3 / a - b\1/2 2 / a - b\1/2 2 / a - b\1/2 2 3 / a - b\1/2 2
- 3 a |- -----| b cos(x) + 2 a |- -----| h cos(x) + h cos(x) |- -----| b - |- -----| b h cos(x) + h |- -----| b cos(x) + a cos(x) |- -----| b
\ a + b/ \ a + b/ \ a + b/ \ a + b/ \ a + b/ \ a + b/

2 2 / a - b\1/2 2 2 / a - b\1/2 / a - b\1/2 2 2 / a - b\1/2 2 2 2 / a - b\1/2
+ 2 b cos(x) a |- -----| - 3 b cos(x) a |- -----| + a |- -----| h cos(x) - 2 h cos(x) |- -----| b + h cos(x) |- -----| b
\ a + b/ \ a + b/ \ a + b/ \ a + b/ \ a + b/

3 / a + b cos(x) \1/2 1/2 2 / a + b cos(x) \1/2 1/2
- b cos(x) |--------------------| %3 EllipticF(%1, %2) sin(x) + b cos(x) a |--------------------| %3 EllipticF(%1, %2) sin(x)
\(a + b) (1 + cos(x/ \(a + b) (1 + cos(x/

2 / a + b cos(x) \1/2 1/2 / a - b\1/2 3 / a - b\1/2
+ 2 h cos(x) a |--------------------| %3 EllipticF(%1, %2) sin(x) - 4 a |- -----| b h cos(x) + a |- -----| cos(x)
\(a + b) (1 + cos(x/ \ a + b/ \ a + b/

/ a + b cos(x) \1/2 1/2 / a + b cos(x) \1/2 1/2 2
- a |--------------------| %3 h EllipticF(%1, %2) b sin(x) - h sin(x) |--------------------| %3 b EllipticF(%1, %2)
\(a + b) (1 + cos(x/ \(a + b) (1 + cos(x/

/ a + b cos(x) \1/2 1/2 2 2 / a + b cos(x) \1/2 1/2 2
- h sin(x) |--------------------| %3 b EllipticF(%1, %2) cos(x) - a cos(x) |--------------------| %3 b EllipticF(%1, %2) sin(x)
\(a + b) (1 + cos(x/ \(a + b) (1 + cos(x/

/ a + b cos(x) \1/2 1/2 2 2 / a + b cos(x) \1/2 1/2
- a sin(x) |--------------------| %3 b EllipticF(%1, %2) - h cos(x) |--------------------| %3 EllipticF(%1, %2) b sin(x)
\(a + b) (1 + cos(x/ \(a + b) (1 + cos(x/

2 / a + b cos(x) \1/2 1/2 2 2 / a - b\1/2 2 / a - b\1/2 / a - b\1/2 2 3 / a - b\1/2
+ b a |--------------------| %3 EllipticF(%1, %2) sin(x) cos(x) - 2 a |- -----| h + b a |- -----| + 2 a |- -----| b cos(x) - a |- -----|
\(a + b) (1 + cos(x/ \ a + b/ \ a + b/ \ a + b/ \ a + b/

2 / a + b cos(x) \1/2 1/2 3 / a + b cos(x) \1/2 1/2 2
+ 2 a sin(x) |--------------------| %3 h EllipticF(%1, %2) - b |--------------------| %3 EllipticF(%1, %2) sin(x) cos(x)
\(a + b) (1 + cos(x/ \(a + b) (1 + cos(x/

/ a + b cos(x) \1/2 1/2 2 3 / a + b cos(x) \1/2 1/2 3 2 / a - b\1/2
+ a |--------------------| %3 h EllipticF(%1, %2) sin(x) + a cos(x) |--------------------| %3 EllipticF(%1, %2) sin(x) + b cos(x) |- -----|
\(a + b) (1 + cos(x/ \(a + b) (1 + cos(x/ \ a + b/

3 3 / a - b\1/2 / a + b cos(x) \1/2 1/2 2 2 / a - b\1/2
- b cos(x) |- -----| + a |--------------------| %3 h EllipticF(%1, %2) b sin(x) cos(x) + 3 a cos(x) |- -----| b h
\ a + b/ \(a + b) (1 + cos(x/ \ a + b/

/ a + b cos(x) \1/2 1/2 2 3 / a + b cos(x) \1/2 1/2
- |--------------------| %3 h EllipticF(%1, %2) b sin(x) + a sin(x) |--------------------| %3 EllipticF(%1, %2)
\(a + b) (1 + cos(x/ \(a + b) (1 + cos(x/

2 / a + b cos(x) \1/2 1/2 / a + b cos(x) \1/2 1/2 2
+ h cos(x) a |--------------------| %3 EllipticF(%1, %2) sin(x) + |--------------------| %3 h EllipticE(%1, %2) b sin(x)
\(a + b) (1 + cos(x/ \(a + b) (1 + cos(x/

2 / a + b cos(x) \1/2 1/2 / a + b cos(x) \1/2 1/2 2
- a cos(x) |--------------------| %3 h EllipticE(%1, %2) b sin(x) + 2 cos(x) h sin(x) |--------------------| %3 b EllipticE(%1, %2)
\(a + b) (1 + cos(x/ \(a + b) (1 + cos(x/

2 / a + b cos(x) \1/2 1/2 \ / / / a - b\1/2 1/2
- h sin(x) a |--------------------| %3 EllipticE(%1, %2)| / |(b + h + a) |- -----| (a + h - b) (a + b cos(x sin(x)
\(a + b) (1 + cos(x/ / / \ \ a + b/

3 3 2 2 2 2 2 2 2 2 3 3 1/2\
(b cos(x) + 3 h b cos(x) + 3 a b cos(x) + 6 a h b cos(x) + 3 b h cos(x) + 3 a b cos(x) + 3 a h + 3 a h + h + a ) |
/

/ a - b\1/2
|- -----| (-1 + cos(x
\ a + b/
%1 := --------------------------
sin(x)

/ 2 2 \1/2
|a - b + a h + b h|
%2 := |-------------------|
\(b + h + a) (a - b)/

a + h + b cos(x)
%3 := ------------------------
(b + h + a) (1 + cos(x

mong

покажи свою версию :)

Skilet3d

Видимо вначале стоит сделать стандартную замену t=tg x/2
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