What is the integral of csc(pix)cot(pix)+2 ?

The integral of csc(pix)cot(pix)+2 is -1/pi csc(pix)+2x+C

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integral of csc(pix)cot(pix)+2

\int csc (π x) cot (π x) + 2 d x

- \frac{1}{π} csc (π x) + 2 x + C

Solution steps

\int csc (π x) cot (π x) + 2 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 (π x) cot (π x) d x + \int 2 d x

\int csc (π x) cot (π x) d x = - \frac{1}{π} csc (π x)

\int 2 d x = 2 x

= - \frac{1}{π} csc (π x) + 2 x

Add a constant to the solution

= - \frac{1}{π} csc (π x) + 2 x + C

\int x^{4} 15 + x^{5} d x

\int \frac{e ^{t} + 2}{e ^{t} + 2 t} d t

\int 3 x + 3 d x

\int \frac{6 - 4 x e ^{x}}{x} d x

8 x^{2}

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