1 / | | x | ------------- dx | 2 | x - 4*x + 13 | / 0
/ | | x | 1*------------- dx | 2 | x - 4*x + 13 | /
/ 1*2*x - 4 \ |---------------| /2\ | 2 | |-| x \1*x - 4*x + 13/ \9/ ------------- = ----------------- + -------------- 2 2 2 x - 4*x + 13 / x 2\ |- - + -| + 1 \ 3 3/
/ | | x | 1*------------- dx | 2 = | x - 4*x + 13 | /
/ | / | 1 | 2* | -------------- dx | 1*2*x - 4 | 2 | --------------- dx | / x 2\ | 2 | |- - + -| + 1 | 1*x - 4*x + 13 | \ 3 3/ | | / / --------------------- + ---------------------- 2 9
/ | | 1*2*x - 4 | --------------- dx | 2 | 1*x - 4*x + 13 | / --------------------- 2
2 u = x - 4*x
/ | | 1 | ------ du | 13 + u | / log(13 + u) ------------ = ----------- 2 2
/ | | 1*2*x - 4 | --------------- dx | 2 | 1*x - 4*x + 13 | / 2 \ / log\13 + x - 4*x/ --------------------- = ------------------ 2 2
/ | | 1 2* | -------------- dx | 2 | / x 2\ | |- - + -| + 1 | \ 3 3/ | / ---------------------- 9
2 x v = - - - 3 3
/ | | 1 2* | ------ dv | 2 | 1 + v | / 2*atan(v) -------------- = --------- 9 9
/ | | 1 2* | -------------- dx | 2 | / x 2\ | |- - + -| + 1 | \ 3 3/ / 2 x\ | 2*atan|- - + -| / \ 3 3/ ---------------------- = --------------- 9 3
/ 2 x\ / 2 \ 2*atan|- - + -| log\13 + x - 4*x/ \ 3 3/ C + ------------------ + --------------- 2 3
/ / 2 x\ | / 2 \ 2*atan|- - + -| | x log\13 + x - 4*x/ \ 3 3/ | ------------- dx = C + ------------------ + --------------- | 2 2 3 | x - 4*x + 13 | /
log(10) 2*atan(1/3) log(13) 2*atan(2/3) ------- - ----------- - ------- + ----------- 2 3 2 3
=
log(10) 2*atan(1/3) log(13) 2*atan(2/3) ------- - ----------- - ------- + ----------- 2 3 2 3
Данные примеры также можно применять при вводе верхнего и нижнего предела интегрирования.