Question

这两道题怎么做？有过程解析，谢谢

Answer 1

解：
1、(arctan√x)²+C
2、arctan［f(x)］+C
过程如图

Answer 2

(1)
let
u=arctan√x
du = (1/[2√x.(1+x)] ) dx
∫ arctan√x /[ √x.(1+x) ] dx
=2∫ u du
=u^2 + C
=[arctan√x]^2 +C
(2)

∫f'(x)/[1+(f(x))^2] dx
=∫df(x)/[1+(f(x))^2]
=arctan[f(x) ] + C