What is the integral of csc^2(x)+7 ?

The integral of csc^2(x)+7 is -cot(x)+7x+C

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integral of csc^2(x)+7

\int csc^{2} (x) + 7 d x

- cot (x) + 7 x + C

Solution steps

\int csc^{2} (x) + 7 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 7 d x

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

\int 7 d x = 7 x

= - cot (x) + 7 x

Add a constant to the solution

= - cot (x) + 7 x + C

x \to 6 lim (x^{2} - 7 x + 6)

\frac{\partial}{\partial x} (5 y ln (x))

\frac{d}{d x} (\frac{x ^{3}}{3 - x ^{2}})

\frac{1}{2 x + 10}

y^{^{'}} = 2 x e^{y}