Better Students Ask More Questions.
Hi, can someone please help me to solve and explain this question for me? 1) find the...
2 Answers | add yours
High School Teacher
First we will make substitution `t=e^x.`
`int e^(2x)arctan e^xdx=|(t=e^x),(dt=e^xdx)|=`
`int t arctan t dt`
Now we use partial integration
`=|(u=arctan t,dv=t dt),(du=1/(1+t^2),v=t^2/2)|=`
`t^2/2 arctan t- 1/2int t^2/(1+t^2)=`` `
`t^2/2 arctan t- 1/2int(1-1/(1+x^2))dt=``1/2(t^2 arctan t-t+arctan t)=`
Now we return our substitution `t=e^x.`
`1/2(e^(2x)arctan e^x-e^x+arctan e^x)` <-- Your solution
Posted by tiburtius on April 23, 2013 at 7:27 PM (Answer #1)
Join to answer this question
Join a community of thousands of dedicated teachers and students.