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

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

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

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

- cot (\frac{x}{2}) + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = tan (\frac{x}{2})

= - \frac{1}{tan ( \frac{x}{2} )}

Use the basic trigonometric identity:

\frac{1}{tan ( x )} = cot (x)

= - cot (\frac{x}{2})

Add a constant to the solution

= - cot (\frac{x}{2}) + C

\int tan (\frac{1}{2} x) d x

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\int 7 x x d x

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