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

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

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

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

sin (x) + x + C

Solution steps

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

Rewrite using trig identities

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

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

\int 1 d x = x

= sin (x) + x

Add a constant to the solution

= sin (x) + x + C

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