How do you evaluate the definite integral #int 2/(x+1)^2# from #[0,3]#?

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Answer 1 · 2016-08-30T17:26:00

#int_0^3 2/(x+1)^2dx=3/2#

Use the substitution method as follows :

Let #u=x+1#

#therefore du=dx#

The limits of integration will then change as follows :

#x=0 => u=1 and x=3 => u = 4#

Hence the original integral may be written as

#int_0^3 2/(x+1)^2dx=2 int_1^4 1/u^2 du#

#=-2[1/u]_1^4#

#=-2(1/4-1)#

#=3/2#