Question
Evaluate the integral. ∫arctan(√x) dx
Answers
Leo Galleguillos
Any idea how to get started?
Damon
if z = x^.5
dz = .5 x^-.5 dx
or
dx = 2 x^.5 dz = 2 z dz
and you have
2∫ z arctan(z) dz
but
http://www.wolframalpha.com/input/?i=integrate+z+tan%5E-1+z+dz
so
(z^2+1) arc tan (z) - z + constant
now put z = x^.5 back in
dz = .5 x^-.5 dx
or
dx = 2 x^.5 dz = 2 z dz
and you have
2∫ z arctan(z) dz
but
http://www.wolframalpha.com/input/?i=integrate+z+tan%5E-1+z+dz
so
(z^2+1) arc tan (z) - z + constant
now put z = x^.5 back in