Math CentralQuandaries & Queries


Question from Akilan, a student:

how to integrate these (tan x)^6(sec x)^4 and sinh(x)(cosh(x))^2.

Please send me how to do this question. Having exams on Monday. Please help.


Since sec2 x = 1 + tan2 x you can write

tan6 x sec4 x = tan6 x (sec2 x)(sec2 x) = tan6 x (1 + tan2 x) sec2 x

Now a substitution u = tan x will convert the integrand to a polynomial in u.

For the second integral try the substitution u = cosh x.


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