Use the integral identity:

Question

∫(a-1) (1/(1+x^2))dx=∫(1-1/a) (1/(1+u^2))du
for a>1 to show that:
arctan(a)+arctan(1/a)=π/2

Answer 1

after the integration, you have

arctan(1) - arctan(a) = arctan(1/a) - arctan(1)

π/4 - arctan(a) = arctan(1/a) - π/4

rearrange the terms and you're done.