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

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

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integral of x-csc(x)cot(x)

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

\frac{x ^{2}}{2} + csc (x) + C

Solution steps

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

\int x d x = \frac{x ^{2}}{2}

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

= \frac{x ^{2}}{2} - (- csc (x))

Simplify

= \frac{x ^{2}}{2} + csc (x)

Add a constant to the solution

= \frac{x ^{2}}{2} + csc (x) + C

\int (sin (7 x)) d x

\frac{d}{d x} (\frac{1}{2} ln (2 x))

\frac{d y}{d t} = (15 - \frac{3 y}{360 - 2 t})

\frac{\partial}{\partial v} (u cos (v))

f (x) = 2 x^{2} - 6 x

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