I really need some help with these trig substitution problems. Please write the u and du values for each. I'd really really appreciate it !
1) Integrate [e^x/(e^2x +1)] dx
2) Integrate [X^5 (lnx)] dx
3) Integrate [sinx*cosx] dx
Thank you Again !!
For 1, we can divide both sides by e^x to get:
∫ 1 / (e^x + e^-x) . dX
Have you been taught that cosh(x) = 0.5 (e^x + e^-x)?
So we have:
∫ 1 / 2cosh(x) . dx
= 0.5 ∫ 1 / cosh(x) . dx
= 0.5 ∫ sech(x) . dx
Are you able to go on from here or have I just made it even more complicated?