What is the integral of 3csc^2(x) ?

The integral of 3csc^2(x) is -3cot(x)+C

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integral of 3csc^2(x)

\int 3 csc^{2} (x) d x

- 3 cot (x) + C

Solution steps

\int 3 csc^{2} (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int csc^{2} (x) d x

Use the common integral:

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

= 3 (- cot (x))

Simplify

= - 3 cot (x)

Add a constant to the solution

= - 3 cot (x) + C

y^{^{'}} + cot (x) y - x e^{x} = 0

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

d er i v a t i v e (10 x^{2} - 20 x + 20) e^{x}

d er i v a t i v e y = 4 e^{2 x}

\int_{0}^{4} 0.125 x d x