What is the integral of (csc^2(x)+4) ?

The integral of (csc^2(x)+4) is -cot(x)+4x+C

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integral of (csc^2(x)+4)

\int (csc^{2} (x) + 4) d x

- cot (x) + 4 x + C

Solution steps

\int csc^{2} (x) + 4 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 4 d x

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

\int 4 d x = 4 x

= - cot (x) + 4 x

Add a constant to the solution

= - cot (x) + 4 x + C

\frac{d}{d x} (x^{2} \cdot e^{2 x})

\int \frac{2 ^{2 x}}{1 + 2 ^{2 x}} d x

t \frac{d y}{d t} + 4 y = t^{2}

x y^{2} y^{^{'}} = y^{3} - 5 x^{3}, y (1) = 2

f (x) = - x^{2} + 4

What is the integral of (csc^2(x)+4) ?
The integral of (csc^2(x)+4) is -cot(x)+4x+C