Integral #int(tg^2x+tg^4x)dx# ?

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#int(tg^2x+tg^4x)dx#

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Answer 1 · 2018-05-08T08:20:59

See below

We will use the reduction formula

#inttan^nxdx=tan^(n-1)x/(n-1)-inttan^(n-2)xdx#

For n=2, we have

#inttan^2xdx=tanx/1-inttan^0xdx=tanx-x+C_0#

For n=4, we have

#inttan^4xdx=tan^3x/3-inttan^2xdx=tan^3x/3-tanx+x+C_1#

Adding both results

#int(tan^2x+tan^4x)dx=canceltanx-cancelx+tan^3x/3-canceltanx+cancelx+C_2=tan^3x/3+C_2#