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Grade 12Integral Calculus

evaluate the following integral
∫ 1 + tan x / 1 – tan x dx

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

Ans:
Hello student,
Please find the answer to your question below

$I = \int \frac{1+tanx}{1-tanx}dx$
$I = \int \frac{1+\frac{sinx}{cosx}}{1-\frac{sinx}{cosx}}dx$
$I = \int \frac{cosx+sinx}{cosx-sinx}dx$
$cosx - sinx = t$
$(-sinx - cosx)dx = dt$
$I = \int \frac{-1}{t}dt$
$I = -log(t) + c$
$I = -log(cosx-sinx) + c$

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