Question

Find the integral of (x+1)/(x^2+2x-3) dx from 0 to 1. (Answer: divergent.)

Answer 1

\[I=\int\limits \frac{ x+1 }{ x ^{2}+2x-3 }dx=\frac{ 1 }{2 } \int\limits \frac{ 2x+2 }{x ^{2}+2x-3 }dx\]
\[\int\limits \frac{ 1 }{x }dx=\ln x\]

Answer 2

a liittle bit different, let u = x^2 +2x -3 ---> du = (2x +2 )dx = 2(x+1) dx
and x = 0 , u = -3, x=1 , u = 0
the integral is \[\int_{-3}^0 \frac{ 1 }{2u }du=\frac{1}{2}ln u~~from~~-3~~to~~0\]which is undefined. ---> diverge

Answer 3

@surjithayer Actually, my logic is not good.

Answer 4

because when taking integral of 1/u we got ln|u| , so that the - 3 doesn't affect the result. Please, help

Answer 5

\[at x=0 ,\it \rightarrow -\infty hence diverges\]

Answer 6

Or we can approach by limit? since this is an improper integral, at x = 1, the integrand is undefined, so, we take