What is the integral of 2cos(x)((2csc(x))/(cot(x))) ?

The integral of 2cos(x)((2csc(x))/(cot(x))) is 4x+C

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integral of 2cos(x)((2csc(x))/(cot(x)))

\int 2 cos (x) (\frac{2 csc ( x )}{cot ( x )}) d x

4 x + C

Solution steps

\int 2 cos (x) \frac{2 csc ( x )}{cot ( x )} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot 2 \cdot \int cos (x) \frac{csc ( x )}{cot ( x )} d x

Simplify

= 4 \cdot \int cos (x) \frac{csc ( x )}{cot ( x )} d x

cos (x) \frac{csc ( x )}{cot ( x )} = 1

= 4 \cdot \int 1 d x

Integral of a constant:

\int a d x = a x

= 4 \cdot 1 \cdot x

Simplify

= 4 x

Add a constant to the solution

= 4 x + C

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What is the integral of 2cos(x)((2csc(x))/(cot(x))) ?
The integral of 2cos(x)((2csc(x))/(cot(x))) is 4x+C