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

$$find\int \frac{dt}{1+cost+sint}.$$

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

$$thech.tan\left(\frac{t}{2}\right)=xgive$$$$I=\int \frac{1}{1+\frac{1-x^2}{1+x^2}+\frac{2x}{1+x^2}}\frac{2dx}{1+x^2}$$$$=\int \frac{2dx}{1+x^2+1-x^2+2x}=\int \frac{2dx}{2+2x}=\int \frac{dx}{1+x}$$$$=ln\mid 1+x\mid +\lambda =ln\mid 1+tan\left(\frac{t}{2}\right)\mid +\lambda .$$

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