How do you integrate #(tanx)^8#?

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Answer 1 · 2017-04-13T10:25:39

# tan^7x/7-tan^5x/5+tan^3x/3-tanx+x+C.#

Let, #I=inttan^8xdx=inttan^6x(sec^2x-1)d,#

#=int(tanx)^6d(tanx)-inttan^4x(sec^2x-1)dx,#

#=tan^7x/7-int(tanx)^4d(tanx)+inttan^2x(sec^2x-1)dx,#

#=tan^7x/7-tan^5x/5+int(tanx)^2d(tanx)-inttan^2xdx,#

#=tan^7x/7-tan^5x/5+tan^3x/3-int(sec^2x-1)dx.#

# :. I=tan^7x/7-tan^5x/5+tan^3x/3-tanx+x+C.#

Enjoy Maths.!