What is integral of #tan^2(x) sec^4(x) dx?#

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What is integral of #tan^2(x) sec^4(x) dx?#

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Answer 1 · 2015-02-16T04:05:51

Another way of seeing this problem

#I = inttan^2(x)sec^4(x)dx#
# = inttan^2(x)(1+tan^2(x))^2dx#
#u = tan(x)# then #dx = (du)/(1+u^2)#
#=int(u^2(1+u^2)^2/(1+u^2))du#
#=int(u^2+u^4)du#
#=u^3/3+u^5/5+C#
#I=tan^3(x)/3+tan^5(x)/5+C#

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What is integral of #tan^2(x) sec^4(x) dx?#

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