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

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

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integral of 4csc^2(x)

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

- 4 cot (x) + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

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

= 4 (- cot (x))

Simplify

= - 4 cot (x)

Add a constant to the solution

= - 4 cot (x) + C

f (x) = 4 x^{2} - 2 x + 1

\int \frac{5 x ^{4}}{1 + x ^{5}} d x

f (x) = 2 x + 1, at x = 3

g (t) = tan (cos (2 t))

(- 1, - 1), (1, 5)