What is the integral of-csc^2((7x)/6) ?

The integral of-csc^2((7x)/6) is 6/7 cot((7x)/6)+C

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integral of-csc^2((7x)/6)

\int - csc^{2} (\frac{7 x}{6}) d x

\frac{6}{7} cot (\frac{7 x}{6}) + C

Solution steps

\int - csc^{2} (\frac{7 x}{6}) d x

Take the constant out:

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

= - \int csc^{2} (\frac{7 x}{6}) d x

Apply u-substitution

: \int csc^{2} (u) \frac{6}{7} d u

= - \int csc^{2} (u) \frac{6}{7} d u

Take the constant out:

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

= - \frac{6}{7} \cdot \int csc^{2} (u) d u

Use the common integral:

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

= - \frac{6}{7} (- cot (u))

Substitute back

u = \frac{7 x}{6}

= - \frac{6}{7} (- cot (\frac{7 x}{6}))

Simplify

= \frac{6}{7} cot (\frac{7 x}{6})

Add a constant to the solution

= \frac{6}{7} cot (\frac{7 x}{6}) + C

\int_{0}^{5} \frac{8 t}{( t - 6 ) ^{2}} d t

\int x^{\frac{2}{5}} d x

x \to - 2 lim (e^{2 x - x^{2}})

\frac{d}{d x} (- 2 x^{- 2})

f (x) = \frac{x - 1}{2 - x}, at x = 4

What is the integral of-csc^2((7x)/6) ?
The integral of-csc^2((7x)/6) is 6/7 cot((7x)/6)+C