Calculus Examples

$\int_{a}^{b} \coth (x) d x$

Step 1

The integral of $\coth (x)$ with respect to $x$ is $\ln (| \sinh (x) |)$ .

$\ln (| \sinh (x) |)]_{a}^{b}$

Step 2

Simplify the answer.

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Step 2.1

Evaluate $\ln (| \sinh (x) |)$ at $b$ and at $a$ .

$\ln (| \sinh (b) |) - \ln (| \sinh (a) |)$

Step 2.2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\ln (\frac{| \sinh (b) |}{| \sinh (a) |})$