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Grade 12Integral Calculus

evaluate the following integral
∫ {1 + tan x tan(x +theta)} dx

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

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

$I = \int (1+tanx.tan(x+\theta ))dx$
$I = \int (1+tanx.\frac{tanx+tan\theta }{1-tanxtan\theta })dx$
$I = \int (\frac{1-tanxtan\theta+ tan^2x+tanxtan\theta }{1-tanxtan\theta })dx$
$I = \int (\frac{1+tan^2x }{1-tanxtan\theta })dx$
$I = \int (\frac{sec^2x }{1-tanxtan\theta })dx$
$1-tanxtan\theta = t$
$-sec^{2}x.tan\theta dx = dt$
$I = \frac{-1}{tan\theta }\int \frac{dt}{t}$
$I = \frac{-1}{tan\theta }log(t)+c$
$I = \frac{-1}{tan\theta }log(1-tanx.tan\theta )+c$

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