1 / | | 3*x - 2 | ------- dx | 2 | x + 9 | / 0
Integral((3*x - 1*2)/(x^2 + 9), (x, 0, 1))
/ | | 3*x - 2 | 1*------- dx | 2 | x + 9 | /
1*2*x + 0 3*-------------- /-2 \ 2 |---| 3*x - 2 1*x + 0*x + 9 \ 9 / ------- = ---------------- + -------------- 2 2 2 x + 9 / x \ |- - + 0| + 1 \ 3 /
/ | | 3*x - 2 | 1*------- dx | 2 = | x + 9 | /
/ | | 1 / 2* | -------------- dx | | 2 | 1*2*x + 0 | / x \ 3* | -------------- dx | |- - + 0| + 1 | 2 | \ 3 / | 1*x + 0*x + 9 | | / / - ---------------------- + ---------------------- 9 2
/ | | 1*2*x + 0 3* | -------------- dx | 2 | 1*x + 0*x + 9 | / ---------------------- 2
2 u = x
/ | | 1 3* | ----- du | 9 + u | / 3*log(9 + u) ------------- = ------------ 2 2
/ | | 1*2*x + 0 3* | -------------- dx | 2 | 1*x + 0*x + 9 | / 2\ / 3*log\9 + x / ---------------------- = ------------- 2 2
/ | | 1 -2* | -------------- dx | 2 | / x \ | |- - + 0| + 1 | \ 3 / | / ----------------------- 9
-x v = --- 3
/ | | 1 -2* | ------ dv | 2 | 1 + v | / -2*atan(v) --------------- = ---------- 9 9
/ | | 1 -2* | -------------- dx | 2 | / x \ | |- - + 0| + 1 | \ 3 / /x\ | -2*atan|-| / \3/ ----------------------- = ---------- 9 3
/x\ 2*atan|-| / 2\ \3/ 3*log\9 + x / C - --------- + ------------- 3 2
/ /x\ | 2*atan|-| / 2\ | 3*x - 2 \3/ 3*log\9 + x / | ------- dx = C - --------- + ------------- | 2 3 2 | x + 9 | /
3*log(9) 2*atan(1/3) 3*log(10) - -------- - ----------- + --------- 2 3 2
=
3*log(9) 2*atan(1/3) 3*log(10) - -------- - ----------- + --------- 2 3 2
Use the examples entering the upper and lower limits of integration.