1 / | | x - 2 | ------------ dx | 2 | x - 4*x + 7 | / 0
Integral((x - 2)/(x^2 - 4*x + 7), (x, 0, 1))
/ | | x - 2 | ------------ dx | 2 | x - 4*x + 7 | /
/ 2*x - 4 \ |------------| /0\ | 2 | |-| x - 2 \x - 4*x + 7/ \3/ ------------ = -------------- + -------------------------- 2 2 2 x - 4*x + 7 / ___ ___\ |-\/ 3 2*\/ 3 | |-------*x + -------| + 1 \ 3 3 /
/ | | x - 2 | ------------ dx | 2 = | x - 4*x + 7 | /
/ | | 2*x - 4 | ------------ dx | 2 | x - 4*x + 7 | / ------------------ 2
/ | | 2*x - 4 | ------------ dx | 2 | x - 4*x + 7 | / ------------------ 2
2 u = x - 4*x
/ | | 1 | ----- du | 7 + u | / log(7 + u) ----------- = ---------- 2 2
/ | | 2*x - 4 | ------------ dx | 2 | x - 4*x + 7 | / 2 \ / log\7 + x - 4*x/ ------------------ = ----------------- 2 2
0
___ ___ 2*\/ 3 x*\/ 3 v = ------- - ------- 3 3
True
True
/ 2 \ log\7 + x - 4*x/ C + ----------------- 2
/ | / 2 \ | x - 2 log\x - 4*x + 7/ | ------------ dx = C + ----------------- | 2 2 | x - 4*x + 7 | /
log(4) log(7) ------ - ------ 2 2
=
log(4) log(7) ------ - ------ 2 2
log(4)/2 - log(7)/2
Use the examples entering the upper and lower limits of integration.