Integration of Hyperbolic functions - Algebra-calculators.com

Integration of Hyperbolic functions

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Post published:October 29, 2021
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Integration of Hyperbolic functions

1. Integral involving hyperbolic sine

\int \sinh x d x = \cosh x + C

2. Integral involving hyperbolic cosine

\int \cosh x d x = \sinh x + C

3. Integral involving hyperbolic tangent

\int \tanh x d x = \ln \cosh x + C

4. Integral involving hyperbolic cotangent

\int \coth x d x = \ln | \sinh x | + C

5. Integral involving hyperbolic secant squared

\int {sech}^{2} x d x = \tanh x + C

6. Integral involving hyperbolic cosecant squared

\int {cosech}^{2} x d x = - \coth x + C

7 . \int sech x \tanh x d x = - sech x + C

8 . \int cosech x \coth x d x = - cosech x + C

Example:

Evaluate \int x \cosh (x)^{2} d x

Solution:

Let u = x^{2} . Then, d u = 2 x d x

\int x \cosh (x)^{2} d x = \int \frac{1}{2} \cosh u d u

= \frac{1}{2} \sinh u + C

= \frac{1}{2} \sinh (x^{2}) + C

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