find-dt-1-cost-sint-

Question Number 30179 by abdo imad last updated on 17/Feb/18

f i n d \int \frac{d t}{1 + c o s t + s i n t} .

Commented by abdo imad last updated on 24/Feb/18

t h e c h . t a n (\frac{t}{2}) = x g i v e

I = \int \frac{1}{1 + \frac{1 - x^{2}}{1 + x^{2}} + \frac{2 x}{1 + x^{2}}} \frac{2 d x}{1 + x^{2}}

= \int \frac{2 d x}{1 + x^{2} + 1 - x^{2} + 2 x} = \int \frac{2 d x}{2 + 2 x} = \int \frac{d x}{1 + x}

= l n ∣ 1 + x ∣ + λ = l n ∣ 1 + t a n (\frac{t}{2}) ∣ + λ .