What is the integral from 0 to ln(11) of tanh(x) ?

The integral from 0 to ln(11) of tanh(x) is ln(61/11)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to ln(11) of tanh(x)

\int_{0}^{l n (11)} tanh (x) d x

ln (\frac{61}{11})

Decimal Notation

1.71297 \dots

Solution steps

\int_{0}^{l n (11)} tanh (x) d x

Rewrite using trig identities

= \int_{0}^{l n (11)} \frac{sinh ( x )}{cosh ( x )} d x

Apply u-substitution

: \int_{1}^{\frac{61}{11}} \frac{1}{u} d u

= \int_{1}^{\frac{61}{11}} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{\frac{61}{11}}

Compute the boundaries:

ln (\frac{61}{11})

= ln (\frac{61}{11})

\int_{0}^{1} \frac{( 2 x ^{2} - 5 )}{x} d x

\int_{0}^{1.2} e^{- x} cos (x) d x

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

\int_{1}^{24} 1 + x d x

\int_{z}^{y} \frac{1}{x} d x

What is the integral from 0 to ln(11) of tanh(x) ?
The integral from 0 to ln(11) of tanh(x) is ln(61/11)