What is the integral of csc^2(x)+5 ?

The integral of csc^2(x)+5 is -cot(x)+5x+C

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integral of csc^2(x)+5

\int csc^{2} (x) + 5 d x

- cot (x) + 5 x + C

Solution steps

\int csc^{2} (x) + 5 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 5 d x

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

\int 5 d x = 5 x

= - cot (x) + 5 x

Add a constant to the solution

= - cot (x) + 5 x + C

(1 - x)^{^{'}}

\frac{\partial}{\partial x} (- 2 x e^{- x^{2}})

16 y^{^{''}} - 40 y^{^{'}} + 25 y = 0

sec^{2} (x)

2 y^{^{''}} + 17 y^{^{'}} - 9 y = 0