Question

sec的三次方如何用换元法求不定积分

Answer 1

S(secx)^3dx

=S(cosx/(1-(sinx)^2)dx

=S(1/(1-sinx)(1+sinx))dsinx

令：t=sinx

=S(1/(1+t)(1-t)dt

=1/2*S(1/(1+t)+1/(1-t))dt

=1/2*(ln(1+t)-ln(1-t)+c

=1/2*ln(1+t)/(1-t)+c

=1/2*ln(1+sinx)/(1-sinx)+c