Question

高数题，麻烦写过程，最好是在纸上

Answer 1

如亮或游键图敬磨伍

Answer 2

令x=3sect，则dx=3sect*tantdt.
带入原式
=∫1/(3tant)*3sect*tantdt
=∫sectdt
=∫[cost /冲庆(cost)^2]dt
=∫ 1/[1-(sint)^2]d(sint)
=(1/2)∫散乱握[1/(1-sint)+1/(1+sint)]d(sint)
=(1/2)[-ln|1-sint|+ln|1+sint|]+C
=(1/2)ln|(1+sinx)/(1-sinx)|+C
=(1/2)ln|(1+sinx)^2 / (1-sinx)(1+sinx)|+C
=(1/2)ln|(1+sinx)^2 / (cosx)^2|+C
=ln|(1+sinx)/ (cosx)|+C
=ln|secx+tanx| +C，C为常数

因x=3sect.
则sect=x/3.
tant=√((sect)^2-1)
=√((x/3)^2-1)
=1/3√(x^2-9)

带入=
ln(x/3+1/3√陪改(x^2-9))