Step-by-step Solution

Solve the trigonometric integral $\int\frac{1}{2\sin\left(x\right)\cos\left(x\right)}dx$

Go!
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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

$\frac{x}{2\sin\left(x\right)\cos\left(x\right)}+C_0$