What is the integral from 0 to ln(13) of tanh(x) ?

The integral from 0 to ln(13) of tanh(x) is ln(85/13)

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integral from 0 to ln(13) of tanh(x)

\int_{0}^{l n (13)} tanh (x) d x

ln (\frac{85}{13})

Decimal Notation

1.87770 \dots

Solution steps

\int_{0}^{l n (13)} tanh (x) d x

Rewrite using trig identities

= \int_{0}^{l n (13)} \frac{sinh ( x )}{cosh ( x )} d x

Apply u-substitution

: \int_{1}^{\frac{85}{13}} \frac{1}{u} d u

= \int_{1}^{\frac{85}{13}} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{\frac{85}{13}}

Compute the boundaries:

ln (\frac{85}{13})

= ln (\frac{85}{13})

\int_{0}^{2} \frac{1}{y} d y

\int_{2}^{3} \frac{1}{2} d x

\int_{0}^{3 π} 1 + cos (x) d x

\int_{0}^{0.8} x e^{x} d x

\int_{0}^{1} (\frac{1}{1 + x}) d x

What is the integral from 0 to ln(13) of tanh(x) ?
The integral from 0 to ln(13) of tanh(x) is ln(85/13)