What is the integral of (csc^2(x)+1) ?

The integral of (csc^2(x)+1) is -cot(x)+x+C

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integral of (csc^2(x)+1)

\int (csc^{2} (x) + 1) d x

- cot (x) + x + C

Solution steps

\int csc^{2} (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 csc^{2} (x) d x + \int 1 d x

\int csc^{2} (x) d x = - cot (x)

\int 1 d x = x

= - cot (x) + x

Add a constant to the solution

= - cot (x) + x + C

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

\frac{d y}{d x} + y = \frac{1}{1 + x ^{2}}

\int arctan (5 x - 1) d x

cos (arcsin (x + 5))

\int \frac{x}{9 x ^{2} - 1} d x

What is the integral of (csc^2(x)+1) ?
The integral of (csc^2(x)+1) is -cot(x)+x+C