What is the integral of-csc^2((9x)/8) ?

The integral of-csc^2((9x)/8) is 8/9 cot((9x)/8)+C

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integral of-csc^2((9x)/8)

\int - csc^{2} (\frac{9 x}{8}) d x

\frac{8}{9} cot (\frac{9 x}{8}) + C

Solution steps

\int - csc^{2} (\frac{9 x}{8}) d x

Take the constant out:

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

= - \int csc^{2} (\frac{9 x}{8}) d x

Apply u-substitution

: \int csc^{2} (u) \frac{8}{9} d u

= - \int csc^{2} (u) \frac{8}{9} d u

Take the constant out:

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

= - \frac{8}{9} \cdot \int csc^{2} (u) d u

Use the common integral:

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

= - \frac{8}{9} (- cot (u))

Substitute back

u = \frac{9 x}{8}

= - \frac{8}{9} (- cot (\frac{9 x}{8}))

Simplify

= \frac{8}{9} cot (\frac{9 x}{8})

Add a constant to the solution

= \frac{8}{9} cot (\frac{9 x}{8}) + C

\int e^{u} d u

9 \cdot x^{2} \cdot y^{^{'}} = y^{^{'}} + 7 \cdot x \cdot e^{- y}

f (x) = 6 x^{\frac{4}{3}} - \frac{2}{3} x^{\frac{3}{2}} + x^{2} - 7 x + 1

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

y^{^{''}} - 2 y^{^{'}} - 3 y = e^{- t}

What is the integral of-csc^2((9x)/8) ?
The integral of-csc^2((9x)/8) is 8/9 cot((9x)/8)+C