What is the integral of 2csc(y)(cot(y)-csc(y)) ?

The integral of 2csc(y)(cot(y)-csc(y)) is 2(-csc(y)+cot(y))+C

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integral of 2csc(y)(cot(y)-csc(y))

\int 2 csc (y) (cot (y) - csc (y)) d y

2 (- csc (y) + cot (y)) + C

Solution steps

\int 2 csc (y) (cot (y) - csc (y)) d y

Take the constant out:

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

= 2 \cdot \int csc (y) (cot (y) - csc (y)) d y

Expand

csc (y) (cot (y) - csc (y)) : csc (y) cot (y) - csc^{2} (y)

= 2 \cdot \int csc (y) cot (y) - csc^{2} (y) d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (\int csc (y) cot (y) d y - \int csc^{2} (y) d y)

\int csc (y) cot (y) d y = - csc (y)

\int csc^{2} (y) d y = - cot (y)

= 2 (- csc (y) - (- cot (y)))

Simplify

= 2 (- csc (y) + cot (y))

Add a constant to the solution

= 2 (- csc (y) + cot (y)) + C

x^{3} + 12 x^{2} + 8

\frac{d}{d x} ((x - 2) e^{x})

\frac{d}{d x} (\frac{1}{ln ( x ) + x})

\frac{d}{d x} (\frac{x ^{2}}{2 + x})

x^{2} 1, 0, 1

What is the integral of 2csc(y)(cot(y)-csc(y)) ?
The integral of 2csc(y)(cot(y)-csc(y)) is 2(-csc(y)+cot(y))+C