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