Question

antiderivative of arctan(2x)dx

Answer 1

use integration by parts, let u = arctan(2x), let dv = dx

Answer 2

int(udv) = uv - int(vdu)

Answer 3

got it?

Answer 4

yeah..du=1/1+x^2 right

Answer 5

2/1 + x^2, dont forget the chain rule!

Answer 6

ooh yeah..got it

Answer 7

i guess i have to memorize all the trig identiities and derivitaves and antiderivative..it sux my exam is 2moro

Answer 8

u should get, xarctan(2x) - ln abs(1 _ x^2) + C

Answer 9

1 + x^2

Answer 10

my bad

Answer 11

medal please lol

Answer 12

Alternative method. Let 2x be theta. Make a right triangle of theta where 2x is opposite, 1 is adjacent. New antiderivative is antiderivative of tan of theta. After antiderivative go back to the triangle to change to original values.