Question

evaluate the integral?

Answer 1

\[\int\limits_{-1}^{1} \frac{ 3e ^{acrtan(y)} }{ 1+y^2 } dy\]

Answer 2

u - subbbbbb \c:/

Answer 3

remember your derivative of arctan(x)?

Answer 4

\[\Large\rm \int\limits\limits_{-1}^{1} \frac{ 3e ^{acrtan(y)} }{ 1+y^2 } dy\quad =\quad3\int\limits_{-1}^{1}e^{\color{orangered}{\arctan(y)}}\left(\color{royalblue}{\frac{1}{1+y^2}dy}\right)\]

Answer 5

Rememberrrrrrr? <.<

Answer 6

mmmm i still didn't get it lol i tried u-sub tho. Let me post my work :)

Answer 7

never mind my phone is acting dumb ><

but i tried to get wolfram alpha to help but it coduldnt calculate it

Answer 8

So the derivative of arctan(x) is 1/(1+x^2)