What is the integral of coth^2(x) ?

The integral of coth^2(x) is x-coth(x)+C

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integral of coth^2(x)

\int coth^{2} (x) d x

x - coth (x) + C

Solution steps

\int coth^{2} (x) d x

Rewrite using trig identities

= \int 1 + csch^{2} (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d x + \int csch^{2} (x) d x

\int 1 d x = x

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

= x - coth (x)

Add a constant to the solution

= x - coth (x) + C

\frac{1}{( x ^{2} + 4 ) ^{3}}

x \to 10 lim (5)

y^{^{''}} - 11 y^{^{'}} + 24 y = e^{- 4 t}

\frac{d}{d x} ((4 x - 3)^{\frac{1}{3}})

\frac{\partial}{\partial x} (\frac{1}{( 1 + x ) ^{2}})