Mathematics

Integrate:
$$\int _{ 0 }^{ \pi  }{ \dfrac { dx }{ 5+3cosx }  }$$


SOLUTION

 $$\int 1/5+3cosx. dx$$

use$$ t=tanx/2$$ thus, $$cosx=1-t^2/1+t^2$$ and $$cos^(2)x/2=1/(1+t)^2$$

$$dt/dx=1/2.sec^(2).x/2$$
$$dt/dx=([1+t^2]/2)$$

By substitution, we eliminate cosx etc and get ...
int $$1/5+3cosx. dx = int 2/(8-2t^2). dt$$
=int$$ 1/(4-t^2).dt$$
=$$1/4.ln([2+t]/[2-t]) + C$$

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Subjective Hard Published on 17th 09, 2020
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