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Grade 12Integral Calculus

evaluate the following integral
∫ (1 – cot x) / (1 + cot 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

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

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