Final Answer
$\frac{x}{2\sin\left(x\right)\cos\left(x\right)}+C_0$
Step-by-step explanation
Problem to solve:
$\int\frac{1}{2sin\left(x\right)cos\left(x\right)}dx$
Choose the solving method
1
Take the constant $\frac{1}{2}$ out of the integral
$\frac{1}{2}\int\frac{1}{\sin\left(x\right)\cos\left(x\right)}dx$
2
The integral of a constant is equal to the constant times the integral's variable
$\frac{\frac{1}{2}x}{\sin\left(x\right)\cos\left(x\right)}$
3
Simplify the fraction $\frac{\frac{1}{2}x}{\sin\left(x\right)\cos\left(x\right)}$
$\frac{x}{2\sin\left(x\right)\cos\left(x\right)}$
4
As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$
$\frac{x}{2\sin\left(x\right)\cos\left(x\right)}+C_0$
Final Answer
$\frac{x}{2\sin\left(x\right)\cos\left(x\right)}+C_0$