Question

evaluate integtal(tanx +2cot x)^2dx
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Answer 1

Step-by-step explanation:

(Tanx+2cotx)^2dx

first we use (a+b)^2=a^2+b^2+2ab

y=tan^2x+4cot^2x+4tanx.cotx

y=tan^2x+4cot^2x+4sinx/cosx.cosx/sinx

=tan^2x+4cot^2x+4

=sec^2x-1+4cosec^2x-1+4

=sec^2x+4cosec^2x+2

integrate

=(sec^2x dx)+4(cosec^2x dx)+2(1 dx)

=tanx-4cotx+2x .ans