I’m trying to verify that two different methods of solving an integral are correct, and I’m trying to figure out if the sec(x) formula is equal to the tan(x) one. I know that the tan(x) formula is the correct answer.
Thanks!
#Converting sec^6(x)/6 - sec^4(x)/4 to tan^6(x)/6+tan^4(x)/4
cosmic cargo
ivory olive
yes those 2 are equal up to addition by a constant
s^6/6 - s^4/4 = (t^2 + 1)^3/6 - (t^2 + 1)^2/4 = t^6/6 + 3t^4/6 + 3t^2/6 + 1/6 - t^4/4 - 2t^2/4 - 1/4 = t^6/6 + t^4/2 - t^4/4 + t^2/2 - t^2/2 + 1/6 - 1/4 = t^6/6 + t^4/4 - 1/12
binomial moment
cosmic cargo
omg bro😭
you’re a lifesaver, thank you so much!!
ivory olive
also you can use desmos and see they are vertical shifted versions of each other