What is the integral of csch^2(13x-4/9) ?

The integral of csch^2(13x-4/9) is -1/13 coth(13x-4/9)+C

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integral of csch^2(13x-4/9)

\int csch^{2} (13 x - \frac{4}{9}) d x

- \frac{1}{13} coth (13 x - \frac{4}{9}) + C

Solution steps

\int csch^{2} (13 x - \frac{4}{9}) d x

Apply u-substitution

: \int csch^{2} (u) \frac{1}{13} d u

= \int csch^{2} (u) \frac{1}{13} d u

Take the constant out:

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

= \frac{1}{13} \cdot \int csch^{2} (u) d u

Use the common integral:

\int csch^{2} (u) d u = - coth (u)

= \frac{1}{13} (- coth (u))

Substitute back

u = 13 x - \frac{4}{9}

= \frac{1}{13} (- coth (13 x - \frac{4}{9}))

Simplify

= - \frac{1}{13} coth (13 x - \frac{4}{9})

Add a constant to the solution

= - \frac{1}{13} coth (13 x - \frac{4}{9}) + C

(- 1, - 1), (4, - 6)

6 t^{5}

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x \to 0 lim (\frac{e ^{x} - 1}{7 x})

What is the integral of csch^2(13x-4/9) ?
The integral of csch^2(13x-4/9) is -1/13 coth(13x-4/9)+C