1 / | | 5*x + 3 | -------------- dx | 2 | x + 10*x + 29 | / 0
/ | | 5*x + 3 | 1*-------------- dx | 2 | x + 10*x + 29 | /
1*2*x + 10 5*---------------- /-22 \ 2 |----| 5*x + 3 1*x + 10*x + 29 \ 4 / -------------- = ------------------ + -------------- 2 2 2 x + 10*x + 29 / x 5\ |- - - -| + 1 \ 2 2/
/ | | 5*x + 3 | 1*-------------- dx | 2 = | x + 10*x + 29 | /
/ | | 1 / 11* | -------------- dx | | 2 | 1*2*x + 10 | / x 5\ 5* | ---------------- dx | |- - - -| + 1 | 2 | \ 2 2/ | 1*x + 10*x + 29 | | / / - ----------------------- + ------------------------ 2 2
/ | | 1*2*x + 10 5* | ---------------- dx | 2 | 1*x + 10*x + 29 | / ------------------------ 2
2 u = x + 10*x
/ | | 1 5* | ------ du | 29 + u | / 5*log(29 + u) -------------- = ------------- 2 2
/ | | 1*2*x + 10 5* | ---------------- dx | 2 | 1*x + 10*x + 29 | / 2 \ / 5*log\29 + x + 10*x/ ------------------------ = --------------------- 2 2
/ | | 1 -11* | -------------- dx | 2 | / x 5\ | |- - - -| + 1 | \ 2 2/ | / ------------------------ 2
5 x v = - - - - 2 2
/ | | 1 -11* | ------ dv | 2 | 1 + v | / -11*atan(v) ---------------- = ----------- 2 2
/ | | 1 -11* | -------------- dx | 2 | / x 5\ | |- - - -| + 1 | \ 2 2/ | / /5 x\ ------------------------ = -11*atan|- + -| 2 \2 2/
/ 2 \ /5 x\ 5*log\29 + x + 10*x/ C - 11*atan|- + -| + --------------------- \2 2/ 2
/ | / 2 \ | 5*x + 3 /5 x\ 5*log\29 + x + 10*x/ | -------------- dx = C - 11*atan|- + -| + --------------------- | 2 \2 2/ 2 | x + 10*x + 29 | /
5*log(29) 5*log(40) -11*atan(3) + 11*atan(5/2) - --------- + --------- 2 2
=
5*log(29) 5*log(40) -11*atan(3) + 11*atan(5/2) - --------- + --------- 2 2
Данные примеры также можно применять при вводе верхнего и нижнего предела интегрирования.