Asked by A
Evaluate the integral. ∫arctan(√x) dx
Answers
Answered by
Leo Galleguillos
Any idea how to get started?
Answered by
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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.