Substitution

[14sohngenk]

Help needed with the following function, all I know is that you need to do three substitutions. Thanks for any help! ∫ sinh (tan (cos x)) cosh (tan (cos x)) sec^2(cos x) sin x dx

 

[stapel]

Help needed with the following function, all I know is that you need to do three substitutions. Thanks for any help! ∫ sinh (tan (cos x)) cosh (tan (cos x)) sec^2(cos x) sin x dx

What are your thoughts? What have you tried? How far have you gotten?

Please be complete. Thank you!

 

[HallsofIvy]

The fact that you have "sinh(tan(cos(x))" should make it obvious what the first two substitutions are! And once you have reduced the integrand to sinh(v)cosh(v), the third substitution should also be clear.
(This integral has been set up to make it easy!)