What is the integral of tanh^2(3x) ?

The integral of tanh^2(3x) is x-1/3 tanh(3x)+C

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integral of tanh^2(3x)

\int tanh^{2} (3 x) d x

x - \frac{1}{3} tanh (3 x) + C

Solution steps

\int tanh^{2} (3 x) d x

Rewrite using trig identities

= \int 1 - sech^{2} (3 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} (3 x) d x

\int 1 d x = x

\int sech^{2} (3 x) d x = \frac{1}{3} tanh (3 x)

= x - \frac{1}{3} tanh (3 x)

Add a constant to the solution

= x - \frac{1}{3} tanh (3 x) + C

\frac{d}{d z} (e^{x z})

\frac{\partial}{\partial x} (- 2 (y + 1) x^{- 3})

2 sin (x) y^{^{'}} + y cos (x) = y^{2} cos (x)

\frac{d}{d x} (\frac{4}{3} tan (x))

\frac{d x}{d t} = \frac{x ^{2} + t t ^{2} + x ^{2}}{t x}

What is the integral of tanh^2(3x) ?
The integral of tanh^2(3x) is x-1/3 tanh(3x)+C