What is the integral of 6csc^2(x) ?

The integral of 6csc^2(x) is -6cot(x)+C

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integral of 6csc^2(x)

\int 6 csc^{2} (x) d x

- 6 cot (x) + C

Solution steps

\int 6 csc^{2} (x) d x

Take the constant out:

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

= 6 \cdot \int csc^{2} (x) d x

Use the common integral:

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

= 6 (- cot (x))

Simplify

= - 6 cot (x)

Add a constant to the solution

= - 6 cot (x) + C

\frac{1}{3} x^{3}

y = - x^{2} + 3 x + 1, y = - x + 1

x \to 0 lim (- 22)

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

x \to 0 lim (\frac{( x ^{2} - x )}{x})