What is the integral of sin(x)(csc(x)+cot(x)) ?

The integral of sin(x)(csc(x)+cot(x)) is x+sin(x)+C

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integral of sin(x)(csc(x)+cot(x))

\int sin (x) (csc (x) + cot (x)) d x

x + sin (x) + C

Solution steps

\int sin (x) (csc (x) + cot (x)) d x

Rewrite using trig identities

= \int 1 + cos (x) d x

Apply the Sum Rule:

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

= \int 1 d x + \int cos (x) d x

\int 1 d x = x

\int cos (x) d x = sin (x)

= x + sin (x)

Add a constant to the solution

= x + sin (x) + C

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What is the integral of sin(x)(csc(x)+cot(x)) ?
The integral of sin(x)(csc(x)+cot(x)) is x+sin(x)+C