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

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

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integral of tanh^2(x)

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

x - tanh (x) + C

Solution steps

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

Rewrite using trig identities

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

\int 1 d x = x

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

= x - tanh (x)

Add a constant to the solution

= x - tanh (x) + C

\int \frac{1}{( x ^{2} - 81 ) ^{2}} d x

\frac{d}{d x} (ln ((e^{3})^{3}))

x \to - 4 + lim (\frac{3 - 8 x}{x + 4})

f (x) = \frac{10}{( 1 - x ) ^{3}}

x \to 0 lim ((3 x - 2)^{4})