What is the integral of tanh^2(u) ?

The integral of tanh^2(u) is u-tanh(u)+C

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integral of tanh^2(u)

\int tanh^{2} (u) d u

u - tanh (u) + C

Solution steps

\int tanh^{2} (u) d u

Rewrite using trig identities

= \int 1 - sech^{2} (u) d u

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 u - \int sech^{2} (u) d u

\int 1 d u = u

\int sech^{2} (u) d u = tanh (u)

= u - tanh (u)

Add a constant to the solution

= u - tanh (u) + C

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