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Grade 12Integral Calculus

evaluate
∫ (a tan x + b cot x)^2 dx

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int (atanx+bcotx)^{2}dx$
$I = \int (a^2tan^2x+b^2cot^2x+2ab)dx$
$I = \int (a^2(sec^2x-1)+b^2(cosec^2x-1)+2ab)dx$
$I = \int a^2sec^2xdx+\int b^2cosec^2xdx-\int (a-b)^2dx$
$I = a^2tanx+\int b^2cosec^2xdx-\int (a-b)^2dx$
$I = a^2tanx- b^2cotx-\int (a-b)^2dx$
$I = a^2tanx- b^2cotx- (a-b)^2x+c$

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