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- PopeLv 72 months agoFavourite answer
Differentiation generally is much easier that integration. That makes checking your integration easier than actually doing it.

d/dx [11tan⁶(x)/6 + 11tan⁸(x)/8 + C]

= 11tan⁵(x) d/dx[tan(x)] + 11tan⁷(x) d/dx[tan(x)]

= 11[tan⁵(x) + tan⁷(x)]sec²(x)

= 11tan⁵(x)[1 + tan²(x)]sec²(x)

= 11tan⁵(x)sec²(x)sec²(x)

= 11tan⁵(x)sec⁴(x)

That looks good.

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