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

The integral of-csc(2x)cot(2x) is 1/2 csc(2x)+C

integral of-csc(2x)cot(2x)

\int - csc (2 x) cot (2 x) d x

\frac{1}{2} csc (2 x) + C

Solution steps

\int - csc (2 x) cot (2 x) d x

Take the constant out:

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

= - \int csc (2 x) cot (2 x) d x

Apply u-substitution

= - \int - \frac{1}{2} d u

Integral of a constant:

\int a d x = a x

= - (- \frac{1}{2}) u

Substitute back

u = csc (2 x)

= - (- \frac{1}{2}) csc (2 x)

Simplify

= \frac{1}{2} csc (2 x)

Add a constant to the solution

= \frac{1}{2} csc (2 x) + C

h \to 0 lim (\frac{( 5 + h ) ^{4} - 625}{h})

d er i v a t i v e 3 e^{3 t}

f^{^{''}} (x) = e^{x}, f^{^{'}} (0) = 2, f (0) = 5

\int (4 x^{3} - 9 x^{2} + 16 x) x^{4} - 3 x^{3} + 8 x^{2} d x

x \to 0 lim (\frac{4 + x - 4 - x}{4 x})

What is the integral of-csc(2x)cot(2x) ?
The integral of-csc(2x)cot(2x) is 1/2 csc(2x)+C