- #1
Dell
- 590
- 0
[tex]\int[/tex]x*arctg(1/x)dx
i have such problems integrating arc functions, don't know why, but they never turn out right,,
by using
[tex]\int[/tex]udv=uv-[tex]\int[/tex]vdu
u=x
du=dx
dv=arctg(1/x)
v=[1/(1+(1/x)2)]*ln|x|
=[x2/1+x2]ln|x|
[tex]\int[/tex]x*arctg(1/x)dx=x*arctg(1/x)-[tex]\int[/tex](x3ln|x|)/(x2+1)dx
now...
i have such problems integrating arc functions, don't know why, but they never turn out right,,
by using
[tex]\int[/tex]udv=uv-[tex]\int[/tex]vdu
u=x
du=dx
dv=arctg(1/x)
v=[1/(1+(1/x)2)]*ln|x|
=[x2/1+x2]ln|x|
[tex]\int[/tex]x*arctg(1/x)dx=x*arctg(1/x)-[tex]\int[/tex](x3ln|x|)/(x2+1)dx
now...