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

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

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integral of-5csc^2(x)

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

5 cot (x) + C

Solution steps

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

Take the constant out:

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

= - 5 \cdot \int csc^{2} (x) d x

Use the common integral:

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

= - 5 (- cot (x))

Simplify

= 5 cot (x)

Add a constant to the solution

= 5 cot (x) + C

x \to - 3 + lim (\frac{x + 4}{x + 3})

x \to + (- 4) lim (∣ x + 4 ∣)

y = 3 x - 4, (2, 5)

3 x \frac{d y}{d x} + y = x

\frac{\partial}{\partial x} (4 e^{x^{2} y} x y)