What is the integral from 0 to ln(14) of tanh(x) ?

The integral from 0 to ln(14) of tanh(x) is ln(197/28)

Popular >

integral from 0 to ln(14) of tanh(x)

\int_{0}^{l n (14)} tanh (x) d x

ln (\frac{197}{28})

Decimal Notation

1.95099 \dots

Solution steps

\int_{0}^{l n (14)} tanh (x) d x

Rewrite using trig identities

= \int_{0}^{l n (14)} \frac{sinh ( x )}{cosh ( x )} d x

Apply u-substitution

: \int_{1}^{\frac{197}{28}} \frac{1}{u} d u

= \int_{1}^{\frac{197}{28}} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{\frac{197}{28}}

Compute the boundaries:

ln (\frac{197}{28})

= ln (\frac{197}{28})

\int_{- 1}^{3} 5 x^{2} - 4 d x

\int_{0}^{1} \frac{5 ^{x}}{5 ^{x} + 1} d x

\int_{0}^{2} 2 x^{2} + 1 x d x

\int_{0}^{1} c x^{2} (1 - x) d x

\int_{0}^{8} 8 e^{- 8 x} d x

What is the integral from 0 to ln(14) of tanh(x) ?
The integral from 0 to ln(14) of tanh(x) is ln(197/28)