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

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

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integral of sin(θ)(cot(θ)+csc(θ))

\int sin (θ) (cot (θ) + csc (θ)) d θ

sin (θ) + θ + C

Solution steps

\int sin (θ) (cot (θ) + csc (θ)) d θ

Rewrite using trig identities

= \int cos (θ) + 1 d θ

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 (θ) d θ + \int 1 d θ

\int cos (θ) d θ = sin (θ)

\int 1 d θ = θ

= sin (θ) + θ

Add a constant to the solution

= sin (θ) + θ + C

\frac{\partial}{\partial x} (6 x + 6 y^{2})

\frac{d}{d x} (x f (x))

(\frac{d y}{d x}) = y + 2 x + 5 - 2

\int \frac{x + 5 x - 4}{15 x + 9} d x

5 y^{^{''}} + y^{^{'}} = - 4 x

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